The Annals of Statistics

Generalization of likelihood ratio tests under nonstandard conditions

H. T. V. Vu and S. Zhou

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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.

Article information

Ann. Statist., Volume 25, Number 2 (1997), 897-916.

First available in Project Euclid: 12 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory 62F03: Hypothesis testing 62F05: Asymptotic properties of tests 62H15: Hypothesis testing
Secondary: 62F05: Asymptotic properties of tests 62J10: Analysis of variance and covariance

Maximum estimators boundary hypothesis tests


Vu, H. T. V.; Zhou, S. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25 (1997), no. 2, 897--916. doi:10.1214/aos/1031833677.

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