A modified likelihood ratio statistic for some nonregular models

Higher-order approximations to the distribution of the likelihood ratio statistic are considered for a class of nonregular models in which the maximum likelihood estimator of the parameter of interest is asymptotically distributed according to an exponential, rather than a normal, distribution. Asymptotic behaviour of this type often arises when the boundary of the support of the distributions under consideration depends on &thgr;. A modified likelihood ratio statistic is proposed that follows its asymptotic distribution to a high degree of approximation, and this statistic is illustrated on several examples. Copyright Biometrika Trust 2004, Oxford University Press.