Asymptotic Efficiencies of Truncated Sequential Tests

Sawasd Tantaratana, H. Vincent Poor

Research output: Contribution to journalArticle

54 Scopus citations

Abstract

Truncation of a sequential test with constant boundaries is considered for the problem of testing a location hypothesis: f(x — θ0) versus f(x — θ1). A test design procedure is developed by using bounds for the error probabilities under the hypothesis and alternative. By viewing the truncated sequential test as a mixture of a sequential probability ratio test and a fixed sample size test, its boundaries and truncation point can be obtained once the degree of mixture is specified. Asymptotically correct approximations for the operating characteristic function and the average sample number function of the resulting test are derived. Numerical results show that an appropriately designed truncated sequential test performs favorably as compared to both the fixed sample size test and the sequential probability ratio test with the same error probabilities. The average sample number function of the truncated test is uniformly smaller than that of the fixed sample size test, and the truncated test maintains average sample sizes under the hypothesis and the alternative that are close to those optimum values achieved by Wald's sequential probability ratio test. More over, the truncated test is more favorable than the sequential probability ratio test in the sense that is has smaller average sample size when the actual location parameter is between θ0 and θ1. This behavior becomes more pronounced as the error probabilities become smaller, implying that the truncated sequential test becomes more favorable as the error probabilities become smaller.

Original languageEnglish (US)
Pages (from-to)911-923
Number of pages13
JournalIEEE Transactions on Information Theory
Volume28
Issue number6
DOIs
StatePublished - Nov 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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