Local linear double and asymmetric kernel estimation of conditional quantiles

Abstract

In this work, we propose and investigate a family of non parametric quantile regression estimates. The proposed estimates combine local linear fitting and double kernel approaches. More precisely, we use a Beta kernel when covariate’s support is compact and Gamma kernel for left-bounded supports. Finite sample properties together with asymptotic behavior of the proposed estimators are presented. It is also shown that these estimates enjoy the property of having finite variance and resistance to sparse design.

Keywords:

• Asymmetric kernels
• Beta kernels
• Double kernel conditional quantile estimation
• Gamma kernels
• Quantile regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08, 62G05 and 62G20

Acknowledgments

The authors wish to express their appreciation to the associate editor, the two referees, and Dr. Farid Beninel for their helpful suggestions and comments.