OPTIMUM PROPERTY OF THE PARTIAL SEQUENTIAL PROBABILITY RATIO TEST.
Abstract
(Xn) is a sequence of i.i.d. r.v.'s with common p.d.f. P sub theta (.), and tests of H sub 0:theta = theta sub 0 against H sub 1:theta = theta sub 1 are discussed. A Partial Sequential Probability Ratio Test (PSPRT) operates exactly like a Wald SPRT, except that n observations are made before the stopping rule is applied. It is shown that in the class C sub n of test procedures requiring at least n observations, (1) the Bayes risk with fixed losses for wrong decision and fixed cost is minimized by a PSPRT, (2) the boundaries of thie PSPRT are those of the Wald SPRT which minimizes the Bayes risk in the class C sub 0, and (3) for all tests having upper bounds alpha and beta on the probabilities of wrong decision, and having finite ASN's, the PSPRT with error probabilities alpha and beta minimizes the ASN at theta = theta sub 0 and theta = theta sub 1. These are the optimum properties which Wald's SPRT has in the class C sub 0. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 15, 1970
- Accession Number
- AD0701685
Entities
People
- Campbell B. Read
Organizations
- Southern Methodist University