Multivariate Mean Parameter Estimation by Using a Partly Exponential Model

SUMMARY A class of partly exponential models is proposed for the regression analysis of multivariate response data. The class is parameterized in terms of the response mean and a general shape parameter. It includes the generalized linear error model and exponential dispersion models as special cases. Maximum likelihood equations for mean parameters are shown to be of the same form as certain generalized estimating equations, and maximum likelihood estimates of mean and shape parameters are asymptotically independent. Some results are given on the efficiency of the estimating equation procedure under misspecification of the response covariance matrix.