Nonlinear regression models with profile nonlinear least squares estimation

Abstract

This paper considers the efficient estimation for a parametric regression model. For parameters estimation, three estimation methods for the parameters are proposed. These estimators are the semi-parametric profile nonlinear least squares estimators, the nonlinear least squares estimators and one-step estimators. We study the asymptotic properties of the proposed estimators, and further discuss their estimation efficiency. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed for parameters. Simulation studies are conducted to compare the proposed estimation methods.

Keywords:

• Estimation efficiency
• Local linear smoothing
• Nonlinear least squared estimator
• Partial linear models

Mathematics Subject Classification (2000):

• 62G05
• 62G08
• 62G20

Acknowledgments

The authors thank the editor, the associate editor, and two referees for their constructive suggestions that helped us to improve the early manuscript.

Additional information

Funding

Yujie Gai’s research was supported by Discipline Construction Funds of Central University of Finance and Economics, and supported by Program for Innovation Research in Central University of Finance and Economics (Grant No. 020250319007).