Adaptive optimal kernel density estimation for directional data

TL;DR

This paper introduces an adaptive, data-driven method for kernel density estimation tailored to directional data, achieving optimal convergence rates and demonstrated through simulations.

Contribution

It proposes a new automatic bandwidth selection rule that adapts to the density's smoothness, improving estimation accuracy for directional data.

Findings

Oracle inequality established for the estimator

Achieves optimal rates of convergence in L2 error

Validated through simulation studies

Abstract

We focus on the nonparametric density estimation problem with directional data. We propose a new rule for bandwidth selection for kernel density estimation. Our procedure is automatic, fully data-driven and adaptive to the smoothness degree of the density. We obtain an oracle inequality and optimal rates of convergence for the L2 error. Our theoretical results are illustrated with simulations.