An Approach to Asymptotic Robustness Analysis of Sequential Tests for Composite Parametric Hypotheses

Abstract

We consider the problem of sequential statistical testing of composite parametric hypotheses. We construct asymptotic expansions for the conditional probabilities of errors and conditional mathematical expectations of the sample size in the presence of “outliers” in observed values. To obtain these results we propose and use a new approach based on the approximation of the generalized likelihood ratio statistic by special Markov chains.