Statistical Inference for a Kind of Nonlinear Regression Model

Abstract

As we all know, statistical inference of linear models has been a hot topic of statistical and econometric research. However, in many practical problems, the variable of interest and covariates are often nonlinear relationship. The performance of the statistical inference using linear models model can be very poor. In this paper, the statistical inference of a nonlinear regression model under some additional restricted conditions is investigated. The restricted estimator for the unknown parameter is proposed. Under some mild conditions, the asymptotic normality of the proposed estimator is established on the basis of Lagrange multiplier and hence can be used to construct the asymptotic confidence region of the regression parameter.