Hypothesis Testing with Finite Statistics.
STANFORD UNIV CA STANFORD ELECTRONICS LABS
Pagination or Media Count:
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
- Statistics and Probability
- Computer Hardware