The Asymptotic Covariance Matrix of the Maximum Likelihood Parameter Estimator in Conditional Poisson Log-linear Models

The asymptotic covariance matrix of the maximum likelihood estimator for the log-linear model is given for a general class of conditional Poisson distributions which include the unconditional Poisson, multinomial and product-multinomial, as special cases. The general conditions are given under which the maximum likelihood covariance matrix is equal to the covariance matrix of an equivalent closed-form weighted least squares estimator.