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June, 1949 Asymptotic Studentization in Testing of Hypotheses
Herman Chernoff
Ann. Math. Statist. 20(2): 268-278 (June, 1949). DOI: 10.1214/aoms/1177730035


A method suggested by Wald for finding critical regions of almost constant size and various modifications are considered. Under reasonable conditions the $s$th step of this method gives a critical region of size $\alpha + R_s(\theta)$ where $\theta$ is the unknown value of the nuisance parameter, $R_s(\theta) = O(N^{-s/2})$ and $N$ is the sample size. The first step of this method gives the region which is obtained by assuming that an estimate $\hat \theta$ of the nuisance parameter is actually equal to $\theta$.


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Herman Chernoff. "Asymptotic Studentization in Testing of Hypotheses." Ann. Math. Statist. 20 (2) 268 - 278, June, 1949.


Published: June, 1949
First available in Project Euclid: 28 April 2007

zbMATH: 0033.07701
MathSciNet: MR30170
Digital Object Identifier: 10.1214/aoms/1177730035

Rights: Copyright © 1949 Institute of Mathematical Statistics

Vol.20 • No. 2 • June, 1949
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