Weak Consistency of Quasi-Maximum Likelihood　Estimates in Multivariate Generalized Linear Models

In this paper, we study quasi-likelihood equation \tsm_i=1^nX_i(y_i-\mu(X_i'\beta))=0　for multivariate generalized linear models (GLMs). Under mild conditions, we prove the　asymptotic existence of the solution \wh\beta_n to the above equation and present　its convergence rate, that is \wh\beta_n-\beta_0=O_p(\underline\lambda_n^-1/2),　where \beta_0 is the true value of parameter \beta and \underline\lambda_n　denotes the smallest eigenvalue of the matrix S_n=\tsm_i=1^nX_iX_i'.