Generalization of likelihood ratio tests under nonstandard conditions

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