A weighted least-squares cross-validation bandwidth selector for kernel density estimation

ABSTRACT

Since the late 1980s, several methods have been considered in the literature to reduce the sample variability of the least-squares cross-validation bandwidth selector for kernel density estimation. In this article, a weighted version of this classical method is proposed and its asymptotic and finite-sample behavior is studied. The simulation results attest that the weighted cross-validation bandwidth performs quite well, presenting a better finite-sample performance than the standard cross-validation method for “easy-to-estimate” densities, and retaining the good finite-sample performance of the standard cross-validation method for “hard-to-estimate” ones.

KEYWORDS:

• Kernel density estimation
• Bandwidth selection
• Cross-validation

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G07
• Secondary 62G20

Acknowledgments

The author expresses his thanks to the reviewers for their comments and suggestions.

Funding

This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.