Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

For the first time, we obtain a general formula for the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n^{-2}$$</EquationSource> </InlineEquation> asymptotic covariance matrix of the bias-corrected maximum likelihood estimators of the linear parameters in generalized linear models, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation> is the sample size. The usefulness of the formula is illustrated in order to obtain a better estimate of the covariance of the maximum likelihood estimators and to construct better Wald statistics. Simulation studies and an application support our theoretical results. Copyright Springer-Verlag Berlin Heidelberg 2014