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April, 1965 Asymptotically Optimal Tests for Multinomial Distributions
Wassily Hoeffding
Ann. Math. Statist. 36(2): 369-401 (April, 1965). DOI: 10.1214/aoms/1177700150


Tests of simple and composite hypothesis for multinomial distributions are considered. It is assumed that the size $\alpha_N$ of a test tends to 0 as the sample size $N$ increases. The main concern of this paper is to substantiate the following proposition: If a given test of size $\alpha_N$ is "sufficiently different" from a likelihood ratio test then there is a likelihood ratio test of size $\leqq\alpha_N$ which is considerably more powerful than the given test at "most" points in the set of alternatives when $N$ is large enough, provided that $\alpha_N \rightarrow 0$ at a suitable rate. In particular, it is shown that chi-square tests of simple and of some composite hypotheses are inferior, in the sense described, to the corresponding likelihood ratio tests. Certain Bayes tests are shown to share the above-mentioned property of a likelihood ratio test.


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Wassily Hoeffding. "Asymptotically Optimal Tests for Multinomial Distributions." Ann. Math. Statist. 36 (2) 369 - 401, April, 1965.


Published: April, 1965
First available in Project Euclid: 27 April 2007

zbMATH: 0135.19706
MathSciNet: MR173322
Digital Object Identifier: 10.1214/aoms/1177700150

Rights: Copyright © 1965 Institute of Mathematical Statistics

Vol.36 • No. 2 • April, 1965
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