Behaviour of Third Order Terms in Quadratic Approximations of LR-Statistics in Multivariate Generalized Linear Models

Abstract

The size of error is investigated when the log-likelihood of multivariate generalized linear models is approximated by a quadratic function. The nonquadratic tail is characterized by analyzing the cubic part of the log-likelihood. In a local analysis simple bounds for that part can be expressed in terms of expectations of the related random variables for arbitrary sample size $N$. Additionally global error bounds are given for the univariate case.