Reducing bias in nonparametric density estimation via bandwidth dependent kernels: $L_1$ view

TL;DR

This paper introduces a new bandwidth-dependent kernel density estimator that enhances bias convergence rates while maintaining variation, improving nonparametric density estimation in the $L_1$ norm without extra assumptions.

Contribution

It proposes a novel bandwidth-dependent kernel density estimator that improves bias convergence rates in $L_1$ without additional assumptions.

Findings

Enhanced bias convergence rates in $L_1$ norm.

Preserves variation convergence rates.

No extra assumptions needed.

Abstract

We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the extant literature.