Sequential testing of parametric hypotheses: performance, robustness and application

Abstract

The problems of sequential testing of hypotheses on parameters of stocha- sic data being observed are considered. An approach to the calculation of the performance characteristics (error probabilities and expected sample number of observations to be used) is developed. Asymptotic expansions for the perfor- mance characteristics are derived under distortions of the hypothetical models for sequential tests from the proposed family of tests. The robust sequential tests are constructed under the minimax risk criterion. The results are used in medicine for the quickest in the mean accessibility detection of a parameter value set in the model with a dynamic parameter.