Accession Number : AD0843984

Title :   Hypothesis Testing with Finite Statistics.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CA STANFORD ELECTRONICS LABS

Personal Author(s) : Cover, Thomas M.

Report Date : AUG 1968

Pagination or Media Count : 24

Abstract : Let X sub 1, X sub 2,... be a sequence of i.i.d. r.v.'s drawn according to an unknown probability measure P. As the data X sub 1, X sub 2,...,X sub n grows with n, standard likelihood ratio decision procedures yield limiting probabilities of error zero in the two-hypothesis test P = P sub 0 vs P = P sub 1. The hypothesis-testing problem is investigated here under the constraint that the data must be summarized after each observation by an m-valued statistic. An algorithm with a 4-valued statistic is described which achieves a limiting probability of error zero in the two-hypothesis testing problem. In common special cases, 2 states are sufficient. Many composite hypothesis tests with close alternatives are easily encompassed within the formulation. (Author)

Descriptors :   (*PROBLEM SOLVING, STATISTICAL ANALYSIS), MEASURE THEORY, DECISION THEORY, PROBABILITY, SET THEORY, DATA STORAGE SYSTEMS, AUTOMATA, THEOREMS.

Subject Categories : Statistics and Probability
      Computer Hardware

Distribution Statement : APPROVED FOR PUBLIC RELEASE