Accession Number : AD0638449
Title : INFORMATION THEORY AND ALTERNATE HYPOTHESIS TESTS.
Corporate Author : RAND CORP SANTA MONICA CALIF
Personal Author(s) : Bussgang,Julian J.
Report Date : SEP 1966
Pagination or Media Count : 36
Abstract : Lindley's concept of the information in an experiment is used to study alternate hypothesis statistical tests. A test is considered to be a combination of a sampling rule and a decision rule which is based on the samples taken. Two information functions are formed for these tests. The information (about the unknown parameter) contained in the samples that are taken and the information contained in the decision they they lead to. The former quantity is always greater than the latter with equality if and only if the test is a sequential probability ratio test (SPRT), neglecting the excess over the boundary. If the information contained in the samples taken in one alternate hypothesis test is greater than the information contained in the samples taken in another than it has greater expected test length. This result together with the result that the SPRT, neglecting excess, is the unique test that utilizes all the information contained in the samples provides a proof of the standard result on the optimal character of the SPRT, for the SPRT neglecting excess. The major purpose of this paper is to develop an information theoretic analysis of alternate hypothesis tests. Using this approach new results on SPRT's and alternate hypothesis tests in general are obtained. (Author)
Descriptors : (*INFORMATION THEORY, *STATISTICAL TESTS), SEQUENTIAL ANALYSIS, PROBABILITY
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE