The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 2 (1997), 897-916.
Generalization of likelihood ratio tests under nonstandard conditions
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.
Ann. Statist., Volume 25, Number 2 (1997), 897-916.
First available in Project Euclid: 12 September 2002
Permanent link to this document
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
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