Adaptive normal reference bandwidth based on quantile for kernel density estimation

Abstract

Bandwidth selection is an important problem of kernel density estimation. Traditional simple and quick bandwidth selectors usually oversmooth the density estimate. Existing sophisticated selectors usually have computational difficulties and occasionally do not exist. Besides, they may not be robust against outliers in the sample data, and some are highly variable, tending to undersmooth the density. In this paper, a highly robust simple and quick bandwidth selector is proposed, which adapts to different types of densities.

Keywords:

• mean integrated squared error
• asymptotically optimal bandwidth
• robust
• outliers
• smoothing

Acknowledgements

This research is partially supported by the National Natural Science Foundation of China (NSFC, Grant No. 10871167). The author would like to thank anonymous referees and the Editor for helpful corrections, comments and suggestions, which improve this paper a lot.