Robustness Evaluation in Sequential Testing of Composite Hypotheses
DOI:
https://doi.org/10.17713/ajs.v37i1.286Abstract
The problem of sequential testing of composite hypotheses is considered. Asymptotic expansions are constructed for the conditional error probabilities and expected sample sizes under “contamination” of the probability distribution of observations. To obtain these results a new approach based on approximation of the generalized likelihood ratio statistic by a specially constructed Markov chain is proposed. The approach is illustrated numerically.
References
Aivazian, S. A. (1959). Comparison of optimal properties of Neyman–Pearson and Wald tests. Probability Theory and its Applications, 4, 86-93.
Bahvalov, N. S. (1973). Numerical Methods (in Russian). Moscow: Nauka.
Ghosh, B. K., and Sen, P. K. (1991). Handbook of Sequential Analysis. New York, Basel, Hong Kong: Marcel Dekker.
Hampel, F., Ronchetti, E., Rousseeuw, P., and Stahel, W. (1986). Robust Statistics. The Approach Based on Influence Functions. New York: John Wiley and Sons.
Huber, P. (1981). Robust Statistics. New York: John Wiley and Sons.
Jennison, C., and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman & Hall / CRC.
Kemeni, J. G., and Snell, J. L. (1959). Finite Markov Chains. New York: JohnWiley and Sons.
Kharin, A. (2002). On robustifying of the sequential probability ratio test for a discrete model under “contaminations”. Austrian Journal of Statistics, 31, 267-277.
Kharin, A., and Kishylau, D. (2005). Robust sequential testing of hypotheses on discrete probability distributions. Austrian Journal of Statistics, 34, 153-162.
Kharin, A. Y., and Kishylau, D. V. (2005). Performance and robustness analysis for sequential testing of hypotheses on parameters of Markov chains (in Russian). Proceedings
of the National Academy of Sciences of Belarus, 4, 30-35.
Lai, T. L. (2001). Sequential analysis: Some classical problems and new challenges. Statistica Sinica, 11, 303-408.
Quang, P. X. (1985). Robust sequential testing. Annals of Statistics, 13, 638-649.
Wald, A. (1947). Sequential Analysis. New York: John Wiley and Sons.
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