Asymptotic results in gamma kernel regression

Abstract

Based on the Gamma kernel density estimation procedure, this article constructs a nonparametric kernel estimate for the regression functions when the covariate are nonnegative. Asymptotic normality and uniform almost sure convergence results for the new estimator are systematically studied, and the finite performance of the proposed estimate is discussed via a simulation study and a comparison study with an existing method. Finally, the proposed estimation procedure is applied to the Geyser data set.

Keywords:

• Gamma kernel regression
• Boundary effect
• Asymptotic normality
• Uniform almost sure convergence.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F35
• Secondary 62G10

Acknowledgment

The authors would like to thank the Editor and the referees for their critical comments that helped to substantially improve the presentation of this article.

Funding

Jianhong Shi’s research is supported by the Natural Science Foundation of Shanxi Province, China (2013011002-1). Weixing Song’s research is partly by the NSF DMS 1205276.