Hypothesis Testing with Finite Statistics.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1968
- Accession Number
- AD0843984
Entities
People
- Thomas M. Cover
Organizations
- Stanford University