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January, 1973 Noncentral Convergence of Wald's Large-Sample Test Statistic in Exponential Families
T. W. F. Stroud
Ann. Statist. 1(1): 161-165 (January, 1973). DOI: 10.1214/aos/1193342393

Abstract

It is shown that under very mild assumptions Wald's large-sample test statistic (quadratic form based on unrestricted maximum likelihood estimators) converges to noncentral chi-square under a sequence of local alternatives of the order $n^{-\frac{1}{2}}$, when the family of distributions is assumed to be of exponential type. This eliminates, for these families, the necessity of invoking the strict regularity conditions of Wald for the purpose of justifying the asymptotic distribution.

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T. W. F. Stroud. "Noncentral Convergence of Wald's Large-Sample Test Statistic in Exponential Families." Ann. Statist. 1 (1) 161 - 165, January, 1973. https://doi.org/10.1214/aos/1193342393

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0253.62018
MathSciNet: MR334364
Digital Object Identifier: 10.1214/aos/1193342393

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 1 • January, 1973
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