Second-order asymptotic expressions for the covariance matrix of maximum likelihood estimators in dispersion models

For the first time, we give an asymptotic formula of order n−2, where n is the sample size, for the covariance matrix of the maximum likelihood estimators of the regression parameters in regular dispersion models. The covariance matrix formula does not involve cumulants of log-likelihood derivatives and is very suitable for computer implementation. The formula yields expressions as special cases for the proper dispersion and exponential family nonlinear models. In particular, it extends the expression obtained by Cordeiro (2004) and corrects a result due to Cordeiro and Santana (2008). Some simulation results are also presented.