On Robustifying of the Sequential Probability Ratio Test for a Discrete Model under “Contaminations”
DOI:
https://doi.org/10.17713/ajs.v31i4.489Abstract
The problem of robustifying of the sequential probability ratio test is considered for a discrete hypothetical model. Exact values for error probabilities and for conditional expected sample sizes are obtained. Asymptotic robustness analysis for these characteristics is performed under “contaminations”. A two-parametric family of modified sequential probability ratio tests is proposed and analyzed to get the robust test by the minimax risk criterion. Numerical experiments illustrate the theoretical results.References
P. Bauer and J. Röhmel. An adaptive method for establishing a dose response relationship. Statistics in Medicine, 14:1595–1607, 1995.
J. Cowden. Statistical Methods in Quality Control. Prentice-hall, Englewood Cliffs, 1957.
R. Durbin. Biological Sequence Analysis. Cambridge University Press, Cambridge, 1998.
B.K. Ghosh. Sequential Tests of Statistical Hypotheses. Addison-Wesley, Reading, 1970.
P. Huber. Robust Statistics. Wiley, New York, 1981.
J.G. Kemeni and J.L. Snell. Finite Markov Chains. Wiley, New York, 1959.
A. Kharin. On asymptotic robustness and performance analysis for sequential hypotheses testing. Proceedings of the International Conference ”Applied Stochastic Models and Data Analysis”, pages 56–61, 2001a.
A. Kharin. Robustness of the sequential probability ratio test for discrete contaminated data. Proceedings of the VI-th International Conference ”Computer Data Analysis and Modeling”, pages 185–191, 2001b.
A. Kharin. An approach to performance analysis of the sequential probability ratio test for simple hypotheses. Proc. of the Belarussian State University, 1:92–96, 2002.
H. Rieder. Robust Asymptotic Statistics. Springer–Verlag, New York, 1994.
D. Siegmund. Error probabilities and average sample number of the sequential probability ratio test. J. Roy. Statist. Soc. Ser. B, 37:394–401, 1975.
D. Siegmund. Sequential Analysis. Tests and Confidence Intervals. Springer–Verlag, New York, 1985.
N. Stockinger and R. Dutter. Robust time series analysis: a survey. Kybernetika, 23, 1987.
A. Wald. Sequential Analysis. John Wiley and Sons, New York, 1947.
M.S. Waterman. Mathematical Methods for DNA Sequences. CRC Press, Boca Raton, 1989.
J. Whitehead. The Design and Analysis of Sequential Clinical Trials. John Wiley and Sons, New York, 1997.
Downloads
Published
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.
How to Cite
