Robustness Analysis in Sequential Statistical Decisions

Alexey Kharin

doi:10.17713/ajs.v49i4.1131

Abstract

The sequential statistical decision making is considered. Performance characteristics (error probabilities and expected sample sizes) for the sequential statistical decision rules (tests) are analysed. Both cases of simple and composite hypotheses are considered. Asymptotic expansions under distortions are constructed for the performance characteristics enabling robust sequential test construction.

Highlights

In many fields of statistical methodology applications, especially in medicine, finance, quality control, problems of statistical decision making are topical (Ghosh and Sen 1991), (Jennison and Turnbull 2000)
To find the optimal dependency is a complicated task, but this scheme of decision making requires a number of observations that is essentially less than what is required by the approach based on fixed sample sizes (see Aivazian (1959))
The problem of robustness analysis (Kharin and Zhuk 1998), (Kharin 1997), (Kharin and Vecherko 2013), (Galinskij and Kharin 1999) for sequential statistical decision making under distortions is an important one

Summary

Introduction

In many fields of statistical methodology applications, especially in medicine, finance, quality control, problems of statistical decision making are topical (Ghosh and Sen 1991), (Jennison and Turnbull 2000). One of the most important problems is to construct decisions providing the requested accuracy on the basis of the minimal information (minimal number of observations). To solve this problem, the sequential approach (Wald 1947), (Lai 2001) is used. The problem of robustness analysis (Kharin and Zhuk 1998), (Kharin 1997), (Kharin and Vecherko 2013), (Galinskij and Kharin 1999) for sequential statistical decision making under distortions is an important one. We systemize some of the results developed by the author for quantitative robustness analysis of sequential decision rules

Case of simple hypotheses

Mathematical model and notation

Distortions

Conclusion