Abstract
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.
Highlights
IntroductionSequential testing of hypotheses (Wald, 1947) is used as an adequate statistical methodology in applications where accuracy (percentage of correct decisions), and the number of observations used is important: medicine (Jennison and Turnbull, 2000), quality control, finance (Ghosh and Sen, 1991), etc
Sequential testing of hypotheses (Wald, 1947) is used as an adequate statistical methodology in applications where accuracy, and the number of observations used is important: medicine (Jennison and Turnbull, 2000), quality control, finance (Ghosh and Sen, 1991), etc.In the applications sequential methods are often applied to “contaminated” data, and this fact results in significant increasing of percentage of incorrect decisions
In this paper we evaluate robustness of the conditional error probabilities and expected sample sizes under “contamination” of the probability distribution of data for composite hypotheses
Summary
Sequential testing of hypotheses (Wald, 1947) is used as an adequate statistical methodology in applications where accuracy (percentage of correct decisions), and the number of observations used is important: medicine (Jennison and Turnbull, 2000), quality control, finance (Ghosh and Sen, 1991), etc. In the applications sequential methods are often applied to “contaminated” data (see Huber, 1981), and this fact results in significant increasing of percentage of incorrect decisions 2002); the optimal properties of sequential procedures (see Aivazian, 1959) become to be broken. Some results on robustness analysis of sequential tests for simple hypotheses case are presented in Quang (1985); A. The robust sequential tests are constructed in case of simple hypotheses for several models of data in A. In this paper we evaluate robustness of the conditional error probabilities and expected sample sizes under “contamination” of the probability distribution of data for composite hypotheses
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