Bandwidth selection for kernel density estimation: a Hermite series-based direct plug-in approach

Abstract

In this paper we propose a new class of Hermite series-based direct plug-in bandwidth selectors for kernel density estimation and we describe their asymptotic and finite sample behaviours. Unlike the direct plug-in bandwidth selectors considered in the literature, the proposed methodology does not involve multistage strategies and reference distributions are no longer needed. The new bandwidth selectors show a good finite sample performance when the underlying probability density function presents not only ‘easy-to-estimate’ but also ‘hard-to-estimate’ distribution features. This quality, that is not shared by other widely used bandwidth selectors as the classical plug-in or the least-square cross-validation methods, is the most significant aspect of the Hermite series-based direct plug-in approach to bandwidth selection.

Keywords:

• Bandwidth selection
• kernel density estimation
• direct plug-in bandwidth selection
• quadratic functionals
• projection methods
• Hermite series

AMS 2010 subject classifications:

• 62G07
• 62G20

Acknowledgments

The author would like to thank an anonymous reviewer for the comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES.