The Annals of Statistics

Generalization of likelihood ratio tests under nonstandard conditions

H. T. V. Vu and S. Zhou

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Abstract

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

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

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031833677

Digital Object Identifier
doi:10.1214/aos/1031833677

Mathematical Reviews number (MathSciNet)
MR1439327

Zentralblatt MATH identifier
0873.62022

Subjects
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

Keywords
Maximum estimators boundary hypothesis tests

Citation

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. https://projecteuclid.org/euclid.aos/1031833677


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