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:

1968-08-01

Pagination or Media Count:

24.0

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