Regression analysis of elliptically symmetric direction data

TL;DR

This paper introduces a comprehensive toolkit for regression analysis of directional data using angular Gaussian distributions, including testing procedures and optimal prediction regions, validated through simulations and real-world applications.

Contribution

It develops new statistical methods for directional data analysis, including testing and prediction techniques, within a flexible angular Gaussian framework.

Findings

Effective testing procedures for isotropy and covariate effects.

Construction of minimal-volume prediction regions.

Successful application to hydrology and bioinformatics data.

Abstract

A comprehensive toolkit is developed for regression analysis of directional data based on a flexible class of angular Gaussian distributions. Informative testing procedures for isotropy and covariate effects on the directional response are proposed. Moreover, a prediction region that achieves the smallest volume in a class of ellipsoidal prediction regions of the same coverage probability is constructed. The efficacy of these inference procedures is demonstrated in simulation experiments. Finally, this new toolkit is used to analyze directional data originating from a hydrology study and a bioinformatics application.