On density estimation with superkernels

Abstract

In this article, we consider the problem of nonparametric density estimation in the case, when the original sample has a large size, but the data are given in a binned form, i.e. in the form of a histogram. Such situations are typical for many physical problems, in particular, in scanning electron microscopy and electron beam lithography. We study how superkernels can be used in such situations. It is shown that superkernels can be essentially superior over conventional kernels not only for very smooth densities. The problem of bandwidth and bin width selection is also considered.

Keywords:

• kernel density estimation
• superkernel
• binned kernel estimator

AMS Subject Classifications :

• 62G07
• 62G20

Acknowledgements

The authors would like to thank the associated editor, two referees and Erin Skaret for their suggestions, which led to significant improvements.