The Austrian Journal of Statistics is an open-access journal (without any fees) including a long history. Its current Impact Factor (Clarivate, Web of Science, 2024) is 0.7. It is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. Special emphasis is on methods and results in official statistics. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews. The current impact factor is 0.7 (Web of Science, Clarivite) and 1.11 (Scopus). We are indexed in Scopus - the Austrian Journal of Statistics is indexed and listed in Scopus, DOAJ, Scimago, ESCI and many other indices. Austrian Journal of Statistics ISNN number is 1026597X
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
Asymptotic Properties of the Location-Scale Regression Estimators for Left Truncated Data
We consider the nonparametric estimation of a heteroscedastic regression model Y = m(X)+σ(X)ϵ, where the error term ϵ is independent of the covariate X, and the functions m and σ are unknown. The response variable Y is allowed to be interfered by a left truncation random variable T. In this work, we propose kernel-estimators for both the location and scale functions m and σ and investigate their strong uniform consistency rates as well as their asymptotic normality. The finite sample performance of the proposed estimator of the regression function m(.) is extensively studied via simulation and indicate that in presence of heteroscedasticity, our new estimator outperforms the classical one (when ignoring heteroscedasticity) and is less sensitive to the presence of outliers. We also investigate the performance of the scale function estimator σ(.). Furthermore, an application to real data demonstrates the effectiveness of our method in terms of prediction accuracy.
Copyright (c) 2026 Saloua Aliouche, Ourida Sadki, Hassiba Benseradj https://creativecommons.org/licenses/by/3.0/
Log-Free Divergence and Covariance Matrix for Compositional Data I: The Affine/Barycentric Approach
The presence of zeroes in Compositional Data (CoDa) is a thorny issue for Aitchison's classical log-ratio analysis. Building upon the geometric approach by (Faugeras (2023)), we study the full CoDa simplex from the perspective of affine geometry. This view allows to regard CoDa as points (and not vectors), naturally expressed in barycentric coordinates. A decomposition formula for the displacement vector of two CoDa points yields a novel family of barycentric dissimilarity measures. In turn, these barycentric divergences allow to define i) Fréchet means and their variants, ii) isotropic and anisotropic analogues of the Gaussian distribution, and importantly iii) variance and covariance matrices. All together, the new tools introduced in this paper provide a log-free, direct and unified way to deal with the whole CoDa space, exploiting the linear affine structure of CoDa, and effectively handling zeroes. A strikingly related approach based on the projective viewpoint and the exterior product is studied in the separate companion paper (Faugeras (2024a)).
Copyright (c) 2026 Olivier Faugeras https://creativecommons.org/licenses/by/3.0/
Nonparametric Estimation for Locally Stationary GARCH Processes with Laplace-Distributed Noise
This paper investigates the Quasi-Maximum Likelihood Estimation (QMLE) method for time-varying GARCH models under the assumption that the innovations follow the standard Laplace distribution. We consider a locally stationary framework. The estimation process is based on a kernel-weighted likelihood approach. We establish the consistency and asymptotic normality of the proposed estimators under regularity assumptions. The efficacy of the method is demonstrated through simulation studies and an application to real-world financial data, highlighting the practical advantages of modeling heavy-tailed innovations with the Laplace distribution.
Copyright (c) 2026 Faris Aissaoui, Khedidja Djeddour-Djaballah https://creativecommons.org/licenses/by/3.0/
Optimum Reliability Acceptance Sampling Plan for Burr Type-XII Distribution under Generalized Hybrid Censoring Scheme
This manuscript focuses on reliability acceptance sampling plans applied to the Burr type-XII distribution within the framework of the generalized hybrid censoring scheme. This study involves determining the sample size (n) and acceptance constant (k1) for given values of producer's and consumer's risks, utilizing the asymptotic normality theory of maximum likelihood estimators for model parameters. Additionally, a Monte-Carlo simulation study is conducted to assess whether the reliability acceptance sampling plans adhere to specified risk levels for finite sample sizes. Optimum reliability acceptance sampling plans are obtained by employing a variance minimization criterion under cost constraints. We have provided the algorithm for the computation of sample size (n) and acceptance constant (k1). Furthermore, the algorithms for computing the optimum reliability acceptance sampling plans under generalized hybrid type-I censoring scheme and generalized hybrid type-II censoring scheme are also provided.
Copyright (c) 2026 Shubham Singh, Arun Kaushik https://creativecommons.org/licenses/by/3.0/
Comparison of the Unit-Lindley and Beta Mixed Model: A Bayesian Perspective
Mixed-effects models are among the most extensively utilized methodologies for evaluating the relationship between correlated outcomes and covariates. The choice of model is contingent upon the nature of the outcome variable. In practical applications, it is frequently encountered that data are both correlated and constrained within the interval (0, 1). The beta mixed model is typically employed to analyze such bounded and correlated data scenarios. However, recent advancements in the unit Lindley (UL) mixed model have highlighted its advantages over the beta mixed model within a classical framework. This study introduces the UL mixed model and compares it to the beta mixed model utilizing a Bayesian approach. The STAN program was employed to conduct the Bayesian analysis and parameter estimation using Hamiltonian Monte Carlo (HMC) under the No-U-Turn Sampler (NUTS). The validity of both models was assessed through Monte Carlo Simulation. Furthermore, both models were applied to real data scenarios. Model comparison was performed using the Leave-One-Out Information Criterion (LOOIC) and the Watanabe-Akaike Information Criterion (WAIC). The results consistently indicated that the beta mixed model is superior to the UL mixed effect model in the Bayesian framework.
Copyright (c) 2026 Nirajan Bam, Pubudu Hitigala Kaluarachchilage https://creativecommons.org/licenses/by/3.0/
Kernel Estimator of the Conditional Hazard Function for Truncated Dependent Data with Functional Regressors
In this paper, we propose a new non-parametric kernel estimator of the conditional hazard function where the explanatory variable takes values in an infinite-dimensional space and the response variable is subject to random left truncation and satisfies the alpha-mixing property. Our main aim is to prove the strong uniform consistency rate for both functional and real arguments of the estimator. Furthermore, the performance of our estimator is evaluated via a simulation study and its practical relevance is illustrated by an application to real-world data.
Copyright (c) 2026 Setti Louiza Affane, Elias Ould-Saïd, Abdelkader Tatachak https://creativecommons.org/licenses/by/3.0/
Bayesian Estimation of Shape Parameter of Gamma Family under Kullback-Leibler Type Loss
In statistical decision-making, the Kullback-Leibler divergence is used as distance measure that depicts the error while measuring the discrepancy between the actual and approximated distributions. In this study, this measure is employed to determine the loss function in case of two-parameter gamma distribution. The Bayes estimate and the associated risk function of the shape parameter alpha are obtained under the derived loss function. In this context, the truncated Poisson distribution has been chosen as the prior knowledge for the unknown parameter. An extensive simulation study is carried out to verify the performance of the Bayes estimator based on the risk values. Additionally, three real life datasets have been analyzed to investigate the applicability of the proposed procedure and the Bayes estimator has shown its efficacy.
Copyright (c) 2026 Proloy Banerjee, Babulal Seal, Shreya Bhunia https://creativecommons.org/licenses/by/3.0/
Boundary Performance of the Beta Kernel Intensity Estimators for Inhomogeneous Poisson Process
We consider the non-parametric estimation of the bivariate intensity function of non-homogeneous Poisson processes in a bounded data. To this end we use the class of kernel estimators with asymmetric beta kernel functions. The beta kernels are non-negative. They change their shape depending on the position on the semi-axis and possess good boundary properties for a wide class of intensity. The theoretical asymptotic properties of the bivariate intensity function like bias and variance are derived. We obtain the optimal bandwidth selection for both estimates as a minimum of the mean integrated squared error (MISE). Numerical studies indicate that the performance of our approach is better, comparing with other bandwidth selection techniques using bias, variance and integrated squared error as criterion. Some applications are made on real datasets.
Copyright (c) 2026 Marcel Sihintoé Badiane, Papa Ngom, Saa Moussa Tenguiano https://creativecommons.org/licenses/by/3.0/
A Bayesian Perspective on Survival Prediction in Colorectal Cancer Using Accelerated Failure Time Models
Accurate survival prediction in colorectal cancer (CRC) is essential for guiding prognosis and optimizing treatment strategies. This study applies a Bayesian Accelerated Failure Time (AFT) modeling framework using three parametric distributions namely Weibull, log-normal and log-logistic to estimate survival times based on clinical characteristics. The models were evaluated using the Widely Applicable Information Criterion (WAIC), Deviance Information Criterion (DIC) and Log Pseudo Marginal Likelihood (LPML). Among the three, the Bayesian log-normal AFT model achieved the best overall fit and predictive performance. Clinical covariates including age, sex, tumor stage, nodal involvement, metastasis status and tumor histology were incorporated to assess their effects on survival time. The analysis confirmed a strong association between advanced nodal stage (N2) and prolonged survival, while estimates for tumor stages, tumor type and sex showed wider credible intervals, indicating greater uncertainty and highlighting the importance of individualized survival modeling. Posterior trace plots confirmed MCMC convergence and parameter stability, reinforcing the model’s reliability. Moreover, The survival probability plots from the Bayesian lognormal AFT model illustrated how age, when combined with key clinical factors impacts the survivability of the patients. This work demonstrates the practical utility of Bayesian AFT models in handling non-proportional hazards and offers a flexible, interpretable framework for individualized survival estimation in CRC. The findings offer a foundation for future studies integrating more complex covariates and advancing personalized oncology.
Copyright (c) 2026 Gitanjali Pradhani, Jonali Gogoi https://creativecommons.org/licenses/by/3.0/
Estimating the Mean of Finite Population under Double Sampling Stratification in the Presence of Non-Response
Estimating finite population mean is the primary concern in many studies, particulary when the non response occurs for some units. This study focuses in estimating the finite population mean using the auxiliary variables under double sampling stratification (DSS) in the presence of non-response which occurs on both the study and the auxiliary variables. A Regression-ratio-in-ratio type exponential strategy is proposed with non-response simultaneously. Expressions for bias and mean square errors (MSE) are derived up-to-first order of approximation. MSE and percentage relative efficiency (PRE) are computed numerically using vrious real data sets. A simulation study is also conducted to verify the performance of estimators. Results indicate that the proposed estimator has the minimum MSE and the maximum PRE compared to competitor estimators. Therefore the proposed estimator is more efficient and is recommended for practical use in future.
Copyright (c) 2025 Syed Muhammad Arsalan, Javid Shabbir, Alamgir Khalil https://creativecommons.org/licenses/by/3.0/
E-Bayesian Inference for Exponential Transformed Inverse Rayleigh Distribution under Progressive Type-II Censoring with Binomial Removals
In this paper, we consider the comparative analysis of Bayes and E-Bayes estimates for the newly developed exponential transformed inverse Rayleigh (ETIR) distribution under the symmetric and asymmetric loss function for the progressive Type-II censoring with binomial removals. The comparison between the proposed estimators have been drawn on the basis of the simulated risks. The study also examines the expected experiment time. The suitability of the model and proposed methodology have been through demonstrated using a precipitation data set.
Copyright (c) 2026 Satya Prakash Mishra, Manoj Kumar, Sanjay Kumar Singh, Anurag Pathak, Sandeep Kumar https://creativecommons.org/licenses/by/3.0/
Modelling Wastewater Data from Austria Using Generalized Additive Models for Location, Scale and Shape (GAMLSS)
Generalized Additive Models for Location, Scale and Shape (GAMLSS) are a flexible alternative to standard regression models, where only the mean of the response variable is modelled in terms of covariates. However, GAMLSS currently are seldom used in statistical applications. In this paper, we analyze data from wastewater measurements in Austria with respect to COVID-19. The goal is to model the viral load in the wastewater in terms of covariates. The results show that both the vaccination rate and the dominant virus variant are important covariates in the analysis of COVID-19 related viral load in the wastewater. Moreover, complex GAMLSS based on the four-parametric Box-Cox t distribution clearly outperformed simpler Generalized Additive Models (GAMs) based on the Gamma distribution. Moreover, GAMLSS show also better predictive performance than GAMs.
Copyright (c) 2026 Roman Pfeiler, Karin Weyermair, Hans Peter Stüger, Sabrina Kuchling, Patrick Hyden, Helga Wagner https://creativecommons.org/licenses/by/3.0/
Gamma and Reciprocal Inverse Gaussian Kernel Estimators for Stress Strength Reliability Model
Several parametric estimation methods have been applied to estimate the reliability of a stress strength model. In this paper, we focus on the nonparametric kernel method and propose two nonparametric estimators based, respectively, on the Gamma and Reciprocal Inverse Gaussian kernels, which are nonnegative kernels, free from boundary bias and achieve the optimal rate of convergence for the mean integrated squared error. We introduce reliability estimators and establish their statistical and asymptotic properties, namely: bias, variance, and mean square error. We also study the selection of the smoothing parameter using the rule-of-thumb and unbiased cross-validation approaches, since it plays an important role in kernel estimation. Finally, a simulation study and an application to real data are carried out to highlight the performance of the proposed estimators.
Copyright (c) 2026 Meriem Medjider, Karima Lagha https://creativecommons.org/licenses/by/3.0/
Log-Free Distance and Covariance Matrix for Compositional Data II: The Projective/Exterior Product Approach
Motivated by finding a way to deal with Compositional Data (CoDa) with or without zeroes in a unified way, we build upon the previous projective geometry viewpoint of Faugeras (2023) and use the tools provided by the exterior product and Grassmann’s algebra. These allow to represent higher dimensional subspaces as linear objects, called multi-vectors, on which the usual Euclidean scalar product can be extended. Applied to CoDa seen as equivalence classes, this allows to define a pseudo-scalar product and pseudo-norm. Depending on the normalization chosen, it is remarkable that the pseudo-norm obtained is either the same barycentric divergence which was derived in Faugeras(2024a) from the affine geometry viewpoint, or becomes a new, orthogonally invariant, genuine distance on the full non-negative CoDa space. These tools are then used to lay the foundations for further statistical analysis of CoDa: we show how the relative position of a pair of CoDa around their means can be decomposed along its components to form exterior covariance, variance and correlation matrices, along with their corresponding global scalar measure of (co)variation. Gaussian distributions, Mahalanobis distance, Fréchet means, etc.. can then be introduced and we sketch their potential statistical applications. Eventually, we establish some connections with various notions encountered in the literature, like divergences based on quantifying inequalities, or canonical angles between subspaces. The paper is preceded by a tutorial on the exterior product, based on intuitive geometric visualization and familiar linear algebra, in order to make the ideas of the paper accessible to non-specialists.
Copyright (c) 2025 Olivier Faugeras https://creativecommons.org/licenses/by/3.0/
Court Surfaces: A Compositional Approach to Tennis Analytics
Compositional data analysis (CoDA) has been extensively applied in fields such as microbiomics, geosciences, and health sciences, yet its potential in sports analytics remains largely untapped. This study applies CoDA to analyze the proportional distribution of matches played on different tennis court surfaces —clay, hard, and grass— and its influence on player rankings and performance. Data from 1,171 Association of Tennis Professionals (ATP) players ranked in the top 100 were examined, revealing significant differences in surface composition across ranking categories (p < 0.001). High-ranked players dedicated 57.8% of their total minutes to hard courts, compared to 32.6% on clay and 9.6% on grass, while lower-ranked players showed a lower proportion of tournaments on hard and a higher proportion on grass. Temporal trends indicated a shift from clay dominance in earlier decades to a predominance of hard courts, with players from the 2010s dedicating 59.8% of their tournament play to hard surfaces. These findings underscore the potential of CoDA to uncover nuanced relationships in sports data, providing actionable insights for optimizing strategies in tennis performance.
Special Issue on Compositional Data Analysis and CoDaWork 2024
Copyright (c) 2025 Pepus Daunis-i-Estadella, Ernest Baiget, Martí Casals https://creativecommons.org/licenses/by/3.0/
Simultaneous Inference in Finite Mixtures of Regression Models
A general framework for simultaneous inference in finite mixtures of generalized linear regression models is presented. Assuming asymptotic normality of the maximum likelihood estimate of all interesting model parameters, confidence regions and p-values using a maximum norm for the multivariate t-statistic are derived. This allows to simultaneously test all regression coefficients whether they are zero. Another application is to test for constant effects across mixture components. Size and power of the new methods are evaluated using artificial data. A real world data set on the productivity of PhD students is used to demonstrate the application of the procedures.
Special Issue. In memorial: Fritz Leisch
Copyright (c) 2025 Friedrich Leisch, Torsten Hothorn https://creativecommons.org/licenses/by/3.0/
Exploring Process Heterogeneity in Environmental Statistics: Examples and Methodological Advances
Environmental models typically rely on stationarity assumptions. However, environmental systems are complex, and processes change over states or seasons, leading to often overlooked heterogeneity. This paper explores methods to incorporate process heterogeneity into statistical models to improve their performance. It considers problems from natural hazards and earth system sciences, demonstrating the effects of process heterogeneity and proposing methodological advances through model extensions. The first problem addresses flood frequency analysis, where floods are generated by different processes in catchment and atmosphere. A mixture model combining peak-over-threshold distributions of flood types can handle this heterogeneity, especially regarding tail heaviness, making it relevant for flood design. The second problem involves minimum flow frequency analysis, with heterogeneity from different summer and winter processes. A mixture distribution model for minima and a copula-based estimator can incorporate seasonal distributions and event dependence, showing significant performance gains for extreme events. The third problem examines process heterogeneity in rainfall models. Clustering event characteristics (e.g., duration, intensity) using Gower's distance and a lightning index helps distinguish between convective and stratiform events, showing potential to enhance rainfall generators. The fourth problem deals with parameter variation in temporal models of environmental variables, using daily streamflow series. A tree-based machine learning model shows that prediction performance and model parameters vary with quantile loss optimization, suggesting the need for different or combined models for full time series in the presence of process heterogeneity. The study highlights the importance of considering process heterogeneity in modeling from the outset and encourages a better understanding of statistical assumptions and the enrichment of physical knowledge in environmental statistics.
Copyright (c) 2025 Gregor Laaha, Johannes Laimighofer, Nur Banu Özcelik, Svenja Fischer https://creativecommons.org/licenses/by/3.0/
Nonparametric Relative Error Regression for LTRC Data
In the present work, we propose a new kernel estimator of the regression function based on the minimization of the mean squared relative error, when the response variable is subject to both random left truncation and right censoring (LTRC). Such variables typically appear in a medical or an engineering life test studies. Under classical conditions we establish the uniform consistency with a rate and the asymptotic normality for the estimator. The performance of the regression function estimator is evaluated on simulated data sets.
Copyright (c) 2025 Latifa Adjoudj, Siham Bey, Zohra Guessoum, Abdelkader Tatachak https://creativecommons.org/licenses/by/3.0/
circlus: An R Package for Circular and Spherical Clustering Using Poisson Kernel-Based and Spherical Cauchy Distributions
This paper introduces circlus, an R package designed for clustering circular and spherical data using Poisson kernel-based (PKB) distributions and spherical Cauchy distributions. The package leverages the general framework for Expectation-Maximization (EM) estimation implemented by package flexmix and provides model drivers for estimating PKB and spherical Cauchy distributions in the components. The drivers implement two approaches for the M-step. The first is a direct maximization approach implemented in C++ via Rcpp, while the second incorporates covariates by solving the M-step using neural networks with the torch package. The package is particularly suited for highdimensional clustering tasks, such as text embeddings on a spherical space, and supportsmodels both with and without covariates. As a case study, we apply circlus to cluster the abstracts of papers co-authored by Fritz Leisch and demonstrate the use with and without the inclusion of co-author count as a covariate.
Copyright (c) 2025 Lukas Sablica, Kurt Hornik, Bettina Grün https://creativecommons.org/licenses/by/3.0/
cellKey - An R Package to Perturb Statistical Tables
National statistical offices (NSIs) routinely publish aggregated data in the form of statistical tables. However, ensuring data privacy is a critical aspect of this process. Anonymization techniques must be applied to these tables to safeguard the privacy of individual data contributors and prevent unauthorized inference about specific units from the published outputs as often required by law. The R package cellKey offers a possible solution to this challenge by implementing a post-tabular perturbation method. This method modifies table cell values after aggregation, ensuring that sensitive information is adequately masked. It is versatile, suitable for both frequency tables and magnitude tables. A key feature of the cellKey package is its ability to maintain consistency across multiple tables that share identical cells. This ensures that anonymized data across different tables remains coherent while still protecting privacy. This approach makes the package especially useful for scenarios involving complex datasets with interrelated tables. The cellKey package is user-friendly and can empower NSIs and other data holders to publish statistical outputs that uphold both data utility and privacy, meeting the growing demands for secure and accessible data dissemination.
Copyright (c) 2025 Bernhard Meindl https://creativecommons.org/licenses/by/3.0/
On an Alternative to Discrete Pareto Model
Here we introduce a novel and versatile discrete distribution as an alternative to discrete Pareto distribution and derive some noteworthy distributional properties. The proposed distribution has some interesting characteristics, such as decreasing hazard rate, unimodality, overdispersion and infinite divisibility. Some characterizations are also obtained. We also consider different estimation procedures for estimating the model parameters, namely: the maximum likelihood, least squares, weighted least squares, Cramer-von Mises methods and compare them using a comprehensive simulation study. Lastly, to illustrate the practical utility of the proposed model, we analyze four real datasets.
Copyright (c) 2025 K Jayakumar, Jiji Jose https://creativecommons.org/licenses/by/3.0/
Demonstrating the Capabilities of the lionfish Software for Interactive Visualization of Market Segmentation Partitions
Market segmentation partitions multivariate data using some clustering algorithm, resulting in some number of homogeneous clusters of consumers for marketing purposes. Often this type of data has no clear cluster structure, that is, no separations or gaps between clusters of points exist, which is why this is considered partitioning rather than clustering. Understanding the differences between the clusters is typically done by examining single features. However, this can be inconclusive as multiple clusters might share similar characteristics on individual features and the market segmentation partition actually defines the clusters based on different linear constraints on the features. To understand what uniquely characterizes a cluster of customers, examining linear combinations of features may be helpful. This article introduces the R package lionfish that provides interactive and dynamic tools to facilitate the exploration and refining of market segmentations. The package integrates tour algorithms that use linear combinations of features to view high-dimensional data, from the tourr package, with Python-powered interactivity, allowing manual control, interactive selection, and multiple linked windows, to support revising the cluster memberships based on visual feedback. The focus is on the widely used k-means clustering algorithm, but the tools also support other algorithms. The utility of the software is demonstrated through three example analyses from the domain of market segmentation. The flexible, user-driven approach provided by package lionfish offers deeper insights into complex market behaviors, enabling more effective segmentation and enhancing strategic decision-making.
Copyright (c) 2025 Matthias Medl, Dianne Cook, Ursula Laa https://creativecommons.org/licenses/by/3.0/
Examining Exams Using Rasch Models and Assessment of Measurement Invariance
Many statisticians regularly teach large lecture courses on statistics, probability, or mathematics for students from other fields such as business and economics, social sciences, psychology, etc. The corresponding exams often use a multiple-choice or single-choice format and are typically evaluated and graded automatically, either by scanning printed exams or via online learning management systems. Although further examinations of these exams would be of interest, these are frequently not carried out. For example a measurement scale for the difficulty of the questions (or items) and the ability of the students (or subjects) could be established using psychometric item response theory (IRT) models. Moreover, based on such a model it could be assessed whether the exam is really fair for all participants or whether certain items are easier (or more difficult) for certain subgroups of students. Here, several recent methods for assessing measurement invariance and for detecting differential item functioning in the Rasch model are discussed and applied to results from a first-year mathematics exam with single-choice items. Several categorical, ordered, and numeric covariates like gender, prior experience, and prior mathematics knowledge are available to form potential subgroups with differential item functioning. Specifically, all analyses are demonstrated with a hands-on R tutorial using the psycho* family of R packages (psychotools, psychotree, psychomix) which provide a unified approach to estimating, visualizing, testing, mixing, and partitioning a range of psychometric models. The paper is dedicated to the memory of Fritz Leisch (1968--2024) and his contributions to various aspects of this work are highlighted.
Copyright (c) 2025 Achim Zeileis https://creativecommons.org/licenses/by/3.0/
Time-Varying Correlations between Selected Exchange Rates: A Robust DCC-GARCH Model Approach
Effective diversification of global portfolios and risk management depends to a large extent on the degree of correlation between the returns of financial assets. The Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroscediency (DCC-GARCH) model addresses the time-varying correlation and volatility among financial assets. The model has a two-step process whereby the volatility of each individual asset is first estimated using the univariate GARCH and the time-varying correlation between those assets is then captured using the DCC framework. Although the DCC-GARCH setup allows for the use of any univariate GARCH model for the variance of each financial asset, when constructing a DCC-GARCH model, most researchers typically use only one univariate GARCH model for all the returns of the financial asset. This study proposes a robust DCC-GARCH model in analyzing the dynamics of time-varying correlations of financial data in which the optimal univariate GARCH models (with the lowest information criteria) for each financial asset are used to build up the DCC-GARCH model. An empirical application of this model in analyzing the time-varying conditional correlation between four exchange rates shows an improvement in results (relative to the information criterion values) compared to the case where only one univariate GARCH model is used to construct the DCC-GARCH model. Standardized residuals in the quasi maximum likelihood estimation (QMLE) procedure for DCC-GARCH parameters, are typically assumed to follow a multivariate Gaussian distribution. One stylized fact of financial data returns is that the residuals are heavy-tailed. We consider the case where the standardized residuals follow a multivariate Gaussian, and the case where they follow either a multivariate Student's t-distribution or a multivariate Laplace distribution. Results show that a robust DCC-GARCH model performs better when the standardized residuals follow a multivariate Student's t-distribution.
Copyright (c) 2025 Bruno Dinga, Jimbo Henri Claver, Cletus Kwa Kum https://creativecommons.org/licenses/by/3.0/
On a Control Chart for Monitoring Rates and Proportions Based on the Standard Two-sided Power Distribution
This paper proposes a new control chart based on the two-parameter standard two-sided power distribution for monitoring rates and proportions, that is, when the quality characteristic of interest belongs to the unit interval (0,1). Control charts based on the well-known beta and Kumaraswamy distributions are usually considered to deal with this kind of data. The standard two-sided power distribution has many similarities to the beta and Kumaraswamy distributions and a number of advantages in terms of tractability. We evaluate and compare the performance of the new control chart with the beta and Kumaraswamy control charts through Monte Carlo simulation experiments. The simulation results reveal that the control chart based on the standard two-sided power distribution outperforms the beta and Kumaraswamy control charts in terms of run length analysis. An empirical application to a real data set is considered to illustrate the new control chart in practice, and comparisons with the two most traditional control charts for rates and proportions (beta and Kumaraswamy) are made.
Copyright (c) 2025 Artur Lemonte https://creativecommons.org/licenses/by/3.0/
Stochastic Restricted Modified Mixed Logistic Estimator
In this study, we introduce a new estimator named the Stochastic Restricted Modified Mixed Logistic Estimator (SRMMLE), which is specifically designed to handle multicollinearity within the framework of stochastic linear restrictions. Further, we enhance the SRMMLE by modifying its coefficients, resulting in four distinct variants: Stochastic Restricted Modified Mixed Logistic Estimator 1 (SRMMLE1), Stochastic Restricted Modified Mixed Logistic Estimator 2 (SRMMLE2), Stochastic Restricted Modified Mixed Logistic Estimator 3 (SRMMLE3), and Stochastic Restricted Modified Mixed Logistic Estimator 4 (SRMMLE4). Based on the mean square error matrix criterion, we establish conditions for the superiority of SRMMLE over existing estimators, such as the Stochastic Restricted Maximum Likelihood Estimator (SRMLE), Stochastic Restricted Ridge Maximum Likelihood Estimator (SRRMLE), Stochastic Restricted Logistic Liu Estimator (SRLLE), and Stochastic Restricted Mixed Liu-Type Estimator (SRMLTE). In the simulation study, we determined the scalar mean square error and the K-fold cross-validated balanced accuracy of the estimators. Further, we present an empirical study and a real data application illustrating the superior performance of the proposed estimator. In particular, the SRMMLE4 outperforms others in terms of scalar mean square error and balanced accuracy.
Copyright (c) 2025 Thayaparan Kayathiri, Manickavasagar Kayanan, Pushpakanthie Wijekoon https://creativecommons.org/licenses/by/3.0/
Optimal Variable Acceptance Sampling Plan under Progressive Type-II Censoring for the Mixture of Exponential-Rayleigh Distributions
Mixture distributions are widely utilized in various practical problems, such as clinical experiments and electronic component life testing. Despite this, the literature does not extensively cover acceptance sampling plans associated with these distributions. In this paper, variable acceptance sampling plans are designed for a mixture of exponential-Rayleigh distributions using partially accelerated life tests. Under progressive Type-II censoring scheme, the maximum likelihood estimators of the unknown parameters of the mixture distribution are derived for Arrhenius and linear life-stress relationships. Based on these relationships, optimal variable sampling plans are formulated. The plan parameters are determined by solving corresponding optimization problems. The study presents numerical findings, a comparative analysis, and sensitivity assessments. Finally, the practical applicability and relevance of the proposed acceptance sampling plans are demonstrated using real-world datasets. These datasets include breast cancer patients' records and failure lifetime data from communication transmitter-receivers in a commercial aircraft.
Copyright (c) 2025 A. M. Mathai, M. Kumar https://creativecommons.org/licenses/by/3.0/
We investigate suitable methods for clustering multivariate ordinal data assuming that the data are collected in surveys with item batteries on the same ordinal answer format and that respondents are to be grouped to characterize different answering patterns and tendencies. We consider heuristic partitioning methods and model-based methods which fit within the flex-scheme proposed by Fritz Leisch for clustering, in combination with different variants of scale handling (numerical coding, nominalization and respecting the ordinal scale). The performance of the methods to extract the true clustering structure is assessed in an illustrative simulation study using artificial data where the number of observations, the number of variables and the number of response levels as well as the difficulty of the clustering problem are systematically varied to highlight in which situations certain methods might be preferable. By extending the flex-scheme with new methods, which we provide in our R package flexord, we help pave the way for future research on ordinal data clustering with even more complex and diverse data-generating processes.
Copyright (c) 2025 Dominik Ernst, Lena Ortega Menjivar, Theresa Scharl, Bettina Grün https://creativecommons.org/licenses/by/3.0/
Robust Filtering for Linear State-space Models with Non-propagating Outliers Following a Mixture of Gaussian Distributions
The problem of recursive filtering in linear state-space models is considered. The solution to this problem is the classical Kalman filter which is optimal in the sense that it minimizes the variance of the estimated states, if the error processes of the state and observation equations are both Gaussian. However, the Kalman filter is well known to be sensitive to outliers, so robustness is an issue. Two approximate conditional-mean (ACM) type filters for vector-valued observations are proposed that generalize existing univariate filters of similar type to the multivariate case. These new ACM-type filters are compared by simulations in a multivariate setting with additive outliers to the classical Kalman filter and the robust least squares (rLS) filter, another approach robustifying the Kalman filter. Additionally, different settings of tuning parameters and their impact are investigated. The results of the simulation experiments show that in the presence of additive outliers the multivariate ACM-type filters not only outperform the classical Kalman filter, as expected, but they also outperform the rLS filter.
Copyright (c) 2025 Bernhard Spangl https://creativecommons.org/licenses/by/3.0/
Reproducibility of statistical simulations is crucial but proved being a challenge in its own right. Recently, lack of reproducibility of important simulation studies stimulated developments of reporting guidelines and specific protocols trying to improve on this situation. The problem, of course, is not new and issues regarding reproducibility of numerical results, for example statistical analyses or simulations, have long been known. Documented lack of progress regarding reproducibility in the past decade naturally leads to the question if problem awareness was not powerful enough to lead to improved reproducibility. As a benchmark case, I tried to reproduce a simulation study in a so far unpublished manuscript by Fritz Leisch and myself. The results show that, time and again, the devil is in the details and much self-discipline and extensive record-keeping and documentation are mission critical.
Copyright (c) 2025 Torsten Hothorn https://creativecommons.org/licenses/by/3.0/