Open Access
August, 1971 On Obtaining Large-Sample Tests from Asymptotically Normal Estimators
T. W. F. Stroud
Ann. Math. Statist. 42(4): 1412-1424 (August, 1971). DOI: 10.1214/aoms/1177693252


This is an extension of Wald's asymptotic test procedure based on unrestricted maximum-likelihood estimators. Wald showed that under certain regularity conditions the test statistic has a limiting central chi-square distribution under the hypothesis and a limiting noncentral chi-square distribution under a sequence of local alternatives. We extend this procedure, allowing it to be based on a broader class of estimators and to obey simpler and less restrictive conditions. Sufficient conditions for validity of the limiting distributions are local twice-differentiability of the left side of the hypothesis and, under a sequence of local alternatives, asymptotic normality of the estimator of the parameter defining the distribution and stochastic convergence (to the appropriate asymptotic value) of the estimator of the covariance matrix. The required asymptotic behavior is verified for the case of independent sampling from two normal distributions and formulas are presented which aid in computing the test statistic.


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T. W. F. Stroud. "On Obtaining Large-Sample Tests from Asymptotically Normal Estimators." Ann. Math. Statist. 42 (4) 1412 - 1424, August, 1971.


Published: August, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0223.62030
MathSciNet: MR290491
Digital Object Identifier: 10.1214/aoms/1177693252

Rights: Copyright © 1971 Institute of Mathematical Statistics

Vol.42 • No. 4 • August, 1971
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