Least squares estimation for nonlinear regression models with heteroscedasticity

Qiying Wang

Abstract

This paper develops an asymptotic theory of nonlinear least squares estimation by establishing a new framework that can be easily applied to various nonlinear regression models with heteroscedasticity. As an illustration, we explore an application of the framework to nonlinear regression models with nonstationarity and heteroscedasticity. In addition to these main results, this paper provides a maximum inequality for a class of martingales, which is of interest in its own right.

Keywords: Nonlinear regression, least squares estimation, nonstationarity, heteroscedasticity, martingale maximum inequality, local time, a mixture of normal distributions.