Ls Estimate Of A Nonlinear Model And Nonlinear Measure

In this paper, we consider the partly nonlinear modelwhere X is a full-rank design matrix.are un-know p-dimensional parameter. g( A ) is continuosly funtion( incude X) , e and Y are 1 random vectors. The method of estimation and measures of nonlinearity are more difficult than the usual linear model. These theories are easy extended to the usual nonlinear model.First, in this paper we study the least squares estimator of the model. A new method about approximation calulate is given, the convergence is proved, we also consider the asympototic property of least square estimator.Second, the curvature measures of nonlinearity are studied and the property of least square estimator are studied by new ways. We give a new method to measure the model's nonlinearity.At last, we extend the mode to unnomal non- full-rank case, and discuss the estimate property of a more generlized separated nonlinear model.