Asymptotic normality in multivariate nonlinear regression and multivariate generalized linear regression models under repeated measurements with missing data

For multivariate nonlinear regression and multivariate generalized linear regression models, with repeated measurements and possible missing values, we derive the asymptotic normality of a general estimating equations estimator of the regression matrix. We also provide consistent estimators of the covariance matrix of the response vectors. In our setting both the response variable and the covariates may be multivariate. Furthermore, the regression parameters are allowed to be dependent on a finite number of time units or some other categorical variable. For example, one may test whether or not the parameter vectors are equal across the different time units. Missing values are permitted, though certainly are not necessary, in order for the asymptotic theory to hold. Herein, any missingness is allowed to depend upon the values of the covariates but not on the response variable. No distributional assumptions are made on the data.