Open Access
March, 1977 On Asymptotically Optimal Tests
G. Tusnady
Ann. Statist. 5(2): 385-393 (March, 1977). DOI: 10.1214/aos/1176343804


Sequences of tests with error $\exp(-nA)$ of the first type are investigated. It is shown that the error of the second type of such a sequence of tests is bounded by $\exp(- nB)$ where $B$ is determined by the Kullback-Leibler information distance of the hypotheses tested. The information distance between the empirical measure and the null-hypothesis on a finite partition of the sample space is proposed to use as a test statistic. A sufficient condition is given which ensures that this test has error of the second type about $\exp(- nB)$ with the best possible $B$. The exact Bahadur slope of the proposed statistic is investigated.


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G. Tusnady. "On Asymptotically Optimal Tests." Ann. Statist. 5 (2) 385 - 393, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0361.62034
MathSciNet: MR431512
Digital Object Identifier: 10.1214/aos/1176343804

Primary: 62G20
Secondary: 62B10

Keywords: asymptotic optimality , exact Bahadur slope , Goodness-of-fit , likelihood ratio , sample entropy

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • March, 1977
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