Density Estimation Using the Sinc Kernel

TL;DR

This paper thoroughly analyzes the sinc kernel density estimator, demonstrating its advantages over other estimators in accuracy, asymptotic behavior, and bandwidth selection, especially for moderate sample sizes and non-smooth densities.

Contribution

It provides a detailed study of the sinc kernel density estimator, highlighting its superior properties and practical benefits over traditional estimators.

Findings

Sinc estimator outperforms others in moderate sample sizes.

It has better asymptotic properties for non-smooth densities.

The sinc estimator simplifies bandwidth selection.

Abstract

This paper deals with the kernel density estimator based on the so-called sinc (or Fourier integral) kernel $K(x)=(\pi x)^{-1}\sin x$. We study in detail both asymptotic and finite sample properties of this estimator. It is shown that, contrary to widespread opinion, the sinc estimator is superior to other estimators in many respects: it is more accurate for quite moderate values of the sample size, has better asymptotics in non-smooth case (the density to be estimated has only first derivative), is more convenient for the bandwidth selection, etc.