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April 1997 Generalization of likelihood ratio tests under nonstandard conditions
H. T. V. Vu, S. Zhou
Ann. Statist. 25(2): 897-916 (April 1997). DOI: 10.1214/aos/1031833677


In this paper, we analyze the statistic which is the difference in the values of an estimating function evaluated at its local maxima on two different subsets of the parameter space, assuming that the true parameter is in each subset, but possibly on the boundary. Our results extend known methods by covering a large class of estimation problems which allow sampling from nonidentically distributed random variables. Specifically, the existence and consistency of the local maximum estimators and asymptotic properties of useful hypothesis tests are obtained under certain law of large number and central limit-type assumptions. Other models covered include those with general log-likelihoods and/or covariates. As an example, the large sample theory of two-way nested random variance components models with covariates is derived from our main results.


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H. T. V. Vu. S. Zhou. "Generalization of likelihood ratio tests under nonstandard conditions." Ann. Statist. 25 (2) 897 - 916, April 1997.


Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0873.62022
MathSciNet: MR1439327
Digital Object Identifier: 10.1214/aos/1031833677

Primary: 62E20 , 62F03 , 62F05 , 62H15
Secondary: 62F05 , 62J10

Keywords: boundary hypothesis tests , Maximum estimators

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 2 • April 1997
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