Signed variable optimal kernel for non-parametric density estimation

TL;DR

This paper introduces a new class of kernels called signed variable optimal kernels for non-parametric density estimation, generalizing the Epanechnikov kernel to improve estimation accuracy.

Contribution

It derives the optimal signed variable kernels for classical density estimation, extending the well-known Epanechnikov kernel to a broader class of kernels.

Findings

Derived the optimal signed variable kernels for density estimation

Generalized the Epanechnikov kernel to a wider class

Improved understanding of kernel choices in density estimation

Abstract

We derive the optimal signed variable in general case kernels for the classical statistic density estimation, which are some generalization of the famous Epanechnikov's ones.