Statistics Papers

Document Type

Journal Article

Date of this Version

1979

Publication Source

The Annals of Statistics

Volume

7

Issue

6

Start Page

1222

Last Page

1230

DOI

10.1214/aos/1176344841

Abstract

Consider the problem of sequential testing of a one sided hypothesis when the risk function is a linear combination of a probability of an error component and an expected cost component. Sobel's results on monotonicity of Bayes procedures and essentially complete classes are extended. Sufficient conditions are given for every Bayes test to be monotone. The conditions are satisfied when the observations are from an exponential family. They are also satisfied for orthogonally invariant tests of a mean vector of a multivariate normal distribution and for scale invariant tests of two normal variances. Essentially complete classes of tests are the monotone tests for all situations where these sufficient conditions are satisfied.

Keywords

sequential tests, hypothesis testing, Bayes test, complete class, monotone likelihood ratio, exponential family, invariant tests

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Date Posted: 27 November 2017

This document has been peer reviewed.