Accession Number : AD0725532

Title :   A Decision-Theoretic Approach to the Problem of Testing a Null Hypothesis.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Rubin,Herman

Report Date : JUN 1971

Pagination or Media Count : 10

Abstract : The author considers the testing of the 'null hypothesis' theta = 0 against the one-dimensional alternative theta not equal to 0. In most problems, the investigator knows that theta = 0 is unreasonable, and would prefer to 'accept' theta = 0 if absolute value of theta is sufficiently small. The assumption is made that the problem is sufficiently regular, that is, that the likelihood function is sufficiently close to that of a sample from a normal distribution with mean theta and variance 1, after normalization if necessary. A mathematical formulation of this problem is given and the solution is investigated. It is shown that a crude procedure based on a 'small sample' treatment and a 'very large sample' treatment can be very bad in the transition region; also, there is not enough information in those treatments to get robust results. (Author)

Descriptors :   (*STATISTICAL TESTS, SAMPLING), DECISION THEORY, STATISTICAL DISTRIBUTIONS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE