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A METHOD FOR DETERMINING THE ASYMPTOTIC EFFICIENCY OF SOME SEQUENTIAL PROBABILITY RATIO TESTS
Author(s) -
Pollard Graham
Publication year - 1990
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1990.tb01012.x
Subject(s) - mathematics , set (abstract data type) , binomial (polynomial) , type i and type ii errors , sequential probability ratio test , type (biology) , binomial distribution , statistics , function (biology) , sample (material) , discrete mathematics , computer science , ecology , chemistry , chromatography , evolutionary biology , biology , programming language
Summary This paper gives a method for decomposing many sequential probability ratio tests into smaller independent components called “modules”. A function of some characteristics of modules can be used to determine the asymptotically most efficient of a set of statistical tests in which a, the probability of type I error equals β, the probability of type II error. The same test is seen also to give the asymptotically most efficient of the corresponding set of tests in which a is not equal to β. The “module” method is used to give an explanation for the super‐efficiency of the play‐the‐winner and play‐the‐loser rules in two‐sample binomial sampling. An example showing how complex cases can be analysed numerically using this method is also given.