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Minimax one-sided Kolmogorov-type distribution-free tests

Part of: Decision theory Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Ronald Pyke
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Abstract

A family of distribution-free statistics along with related tests is defined and properties of its members are studied. These statistics, one of which is the Smirnov-Wald and Wolfowitz statistic, Dn+ yield tests of the one-sided hypotheses. The minimax and maximin tests in this family against a restricted class of alternatives of minimum power are obtained. The connection to a confidence bound of Stringer for the mean is also remarked.

Keywords

KOLMOGOROV-SMIRNOV TESTSMINIMAX TESTSGENERAL EMPIRICAL D. F. ESTIMATORSSTRINGER'S CONFIDENCE BOUND

MSC classification

Primary: 62G10: Hypothesis testing
Secondary: 62C20: Minimax procedures
Type
Part 5 Statistical Studies
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 291 - 308
Copyright
Copyright © Applied Probability Trust 1994 

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