ASYMPTOTIC NORMALITY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE NONLINEAR REGRESSION MODEL WITH NORMAL ERRORS

Asymptotic Properties of the Maximum Likelihood Estimators in the Nonlinear Regression Model with Normal Errors In this paper we consider a set y = (y1,... ,y) of observations, not necessarily independent on identically distributed, whose joint distribution is known to be normal, where both the mean vector p or the covariance matrix 2 may depend on unknown parameters 11,...,y (=y) to be estimated. By putting Pt(Y) = (P(xt.Y) we obtain the nonlinear regression model (t=1,2,...,n), c = N(0,0(y)) Yt = 43(xt'l) ct as a special case. In the present paper we will obtain conditions for the asymptotic normality of a consistent maximum likelihood estimator of y .