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# Accession Number:

## AD0843984

# Title:

## Hypothesis Testing with Finite Statistics.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CA STANFORD ELECTRONICS LABS

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#