Optimal Kernel for Kernel-Based Modal Statistical Methods

TL;DR

This paper identifies an optimal kernel function within a specific class that minimizes asymptotic error in kernel-based modal statistical methods, enhancing estimation accuracy for tasks like mode estimation, regression, and clustering.

Contribution

It introduces a theoretically derived optimal kernel function tailored to improve the accuracy of kernel-based modal statistical methods, considering kernel class and bandwidth.

Findings

The optimal kernel minimizes asymptotic error when combined with an optimal bandwidth.

The study provides a theoretical framework for kernel selection in modal statistical methods.

Empirical validation of the optimal kernel's performance is suggested for future work.

Abstract

Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to the estimation accuracy of these methods. In particular, we theoretically show a (multivariate) optimal kernel that minimizes its analytically-obtained asymptotic error criterion when using an optimal bandwidth, among a certain kernel class defined via the number of its sign changes.