Nearly Optimal Sequential Tests of Composite Hypotheses

Lai, Tze Leung

Ann. Statist., Tome 16 (1988) no. 1, p. 856-886 / Harvested from Project Euclid

Résumé

A simple class of sequential tests is proposed for testing the one-sided composite hypotheses $H_0: \theta \leq \theta_0$ versus $H_1: \theta \geq \theta_1$ for the natural parameter $\theta$ of an exponential family of distributions under the 0-1 loss and cost $c$ per observation. Setting $\theta_1 = \theta_0$ in these tests also leads to simple sequential tests for the hypotheses $H: \theta < \theta_0$ versus $K: \theta > \theta_0$ without assuming an indifference zone. Our analytic and numerical results show that these tests have nearly optimal frequentist properties and also provide approximate Bayes solutions with respect to a large class of priors. In addition, our method gives a unified approach to the testing problems of $H$ versus $K$ and also of $H_0$ versus $H_1$ and unifies the different asymptotic theories of Chernoff and Schwarz for these two problems.

Détail

Publié le : 1988-06-14
Classification:  Bayes sequential tests,  diffusion approximations,  exponential family,  Kullback-Leibler information,  generalized sequential likelihood ratio tests,  boundary crossing probabilities,  62L10,  62L05,  62L15