Weighted nonparametric regression estimation with truncated and dependent data

Abstract

By applying the empirical likelihood method, we construct a new weighted Nadaraya–Watson type estimator of the conditional mean function for a left truncation model. The function includes the regression function, conditional moment as well as conditional distribution function. Under strong mixing assumptions, we obtain the asymptotic normality and weak consistency of the estimator. Finite sample behaviour of the estimator is investigated via simulations too.

Keywords:

• asymptotic normality
• weighted Nadaraya–Watson type estimator
• conditional mean function
• truncated data
• α-mixing

AMS 2000 Subject Classifications::

• 62N01
• 62E20

Acknowledgements

The author was supported by the Grant MTM2011-23204 of the Spanish Ministry of Science and the Project 10PXIB300068PR of the Xunta de Galicia, Spain, and also by the National Natural Science Foundation of China (10871146, 11271286).