Bias reductions for beta kernel estimation

Abstract

The beta kernel estimator for a density with support was discussed by Chen [(1999) ‘Beta Kernel Estimators for Density Functions’, Computational Statistics and Data Analysis, 31, 131–145]. In this paper, when the underlying density has a fourth-order derivative, we improve the beta kernel estimator using the bias correction techniques based on two beta kernel estimators with different smoothing parameters. As a result, we propose new bias corrected beta kernel estimators involving the digamma functions, and then establish their asymptotic properties. Simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.

Keywords:

• nonparametric density estimator
• boundary problem
• beta kernel estimator

Mathematics Subject Classification:

• 62G07
• 62G20

Acknowledgments

The author would like to thank Editor, Professor Iréne Gijbels, Associate Editor, and anonymous referees for their comments on the paper. The author also thanks Professor Yoshihide Kakizawa, Hokkaido University, for his advice. This paper is a part of author's doctoral dissertation (March, 2015; Graduate School of Economics and Business Administration, Hokkaido University).

Disclosure statement

No potential conflict of interest was reported by the author.

Funding

This work was partially supported by the Japan Society for the Promotion of Science (JSPS); Grant-in-Aid for Research Activity Start-up [grant no. 15H06068].

Supplemental data

Supplemental data for this article can be accessed 10.1080/10485252.2015.1110201110.1080/10485252.2015.11102011.