Local polynomial quasi-likelihood regression with truncated and dependent data

Abstract

The local polynomial quasi-likelihood estimation has several good statistical properties such as high minimax efficiency and adaptation of edge effects. In this paper, we construct a local quasi-likelihood regression estimator for a left truncated model, and establish the asymptotic normality of the proposed estimator when the observations form a stationary and α-mixing sequence, such that the corresponding result of Fan et al. [Local polynomial kernel regression for generalized linear models and quasilikelihood functions, J. Amer. Statist. Assoc. 90 (1995), pp. 141–150] is extended from the independent and complete data to the dependent and truncated one. Finite sample behaviour of the estimator is investigated via simulations too.

Keywords:

• quasi-likelihood
• local polynomial
• asymptotic normality
• truncated data
• α-mixing

AMS 2000 Subject Classifications :

• 62N02
• 62E20

Acknowledgements

The authors thank the reviewers for their careful reading and valuable comments. This work was supported by the National Natural Science Foundation of China (10871146, 71171003, 11001070), the scientific research project of education department of Zhejiang Province (Y200906404) and China Postdoctoral Science Foundation (2011M500809), and also by Anhui Provincial Natural Science Foundation, Provincial Natural Science Research Project of Anhui Colleges (KJ2011A032) and Anhui Polytechnic University Foundation for Recruiting Talent (2011YQQ004).