Nonparametric estimation of directional highest density regions

TL;DR

This paper introduces a nonparametric method for estimating highest density regions in directional data using kernel smoothing, with a bootstrap bandwidth selector, validated through simulations and real data applications.

Contribution

It presents a novel plug-in estimator for directional highest density regions and a bootstrap bandwidth selection method, extending set estimation techniques to directional data.

Findings

The proposed estimator performs well in simulations.

Bootstrap bandwidth selector improves estimation accuracy.

Method successfully applied to animal orientation and seismology data.

Abstract

Reconstruction of sets from a random sample of points intimately related to them is the goal of set estimation theory. Within this context, a particular problem is the one related with the reconstruction of density level sets and specifically, those ones with a high probability content, namely highest density regions. We define highest density regions for directional data and provide a plug-in estimator, based on kernel smoothing. A suitable bootstrap bandwidth selector is provided for the practical implementation of the proposal. An extensive simulation study shows the performance of the plug-in estimator proposed with the bootstrap bandwidth selector and with other bandwidth selectors specifically designed for circular and spherical kernel density estimation. The methodology is applied to analyze two real data sets in animal orientation and seismology.