Empirical Density Estimation for Interval Censored Data
DOI:
https://doi.org/10.17713/ajs.v37i1.293Abstract
This paper is concerned with the nonparametric estimation of a density function when the data are incomplete due to interval censoring. The Nadaraya-Watson kernel density estimator is modified to allow description of such interval data. An interactive R application is developed to explore different estimates.
References
Aerts, M., Augustyns, I., and Janssen, P. (1997). Smoothing sparse multinomial data using local polynomial fitting. Journal of Nonparametric Statistics, 8, 127-147.
Baek, J. (1998). A local linear kernel estimator for sparse multinomial data. Journal of the Korean Statistical Society, 27, 515-529.
Goutis, C. (1997). Nonparametric estimation of a mixing density via the kernel method. Journal of the American Statistical Association, 92, 1445-1450.
Hall, P. (1982). The influence of rounding errors on some nonparametric estimators of a density and its derivatives. IAM Journal of Applied Mathematics, 42, 390-399.
Laird, N. (1978). Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73, 805-811.
Liu, L., and Zhu, Y. (2007). Partially projected gradient algorithms for computing nonparametric maximum likelihood estimates of mixing distributions. Journal of Statistical Planning and Inference, 137, 2509-2522.
Nadaraya, E. A. (1964). On estimating regression. Teor. Veroyatn. Primen., 9, 157-159.
Revesz, P. (1972). On empirical density function. Period. Math. Hung., 2, 85-110.
Revesz, P. (1974). On empirical density function. In A. Obretenov (Ed.), Verojatn. stat. metody; mezdunar. letn. sk. teor. verojatn. mat. stat. (p. 63-88). Varna: Bulgarian
Academy of Sciences.
Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics, 27, 832-837.
Schweitzer, M. E., and Severance-Lossin, E. K. (1996). Rounding in earnings data. (Working Paper 9612, Federal Reserve Bank of Cleveland)
Simonoff, J. S. (1983). A penalty function approach to smoothing large sparse contingency tables. Annals of Statistics, 11, 208–218.
Simonoff, J. S. (1995). Smoothing categorical data. Journal of Statistical Planning and Inference, 47, 41-69.
Simonoff, J. S. (1996). Smoothing Methods in Statistics. New York: Springer.
Stoimenova, E., Mateev, P., and Dobreva, M. (2006). Outlier detection as a method for knowledge extraction from digital resources. Rev. Nat. Center Digitization, 9, 1-11.
Downloads
Published
How to Cite
Issue
Section
License
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.