Efficient ANOVA for directional data

TL;DR

This paper develops efficient statistical tests for analyzing variance in directional data, especially geological data, using advanced methods that are valid across a broad class of distributions and demonstrated through simulations and real data.

Contribution

It introduces semi-parametric ANOVA tests for directional data based on Le Cam methodology, improving robustness and efficiency over existing methods.

Findings

Tests are asymptotically optimal within their classes.

Semi-parametric tests outperform parametric ones in finite samples.

Real data application confirms practical utility.

Abstract

In this paper we tackle the ANOVA problem for directional data (with particular emphasis on geological data) by having recourse to the Le Cam methodology usually reserved for linear multivariate analysis. We construct locally and asymptotically most stringent parametric tests for ANOVA for directional data within the class of rotationally symmetric distributions. We turn these parametric tests into semi-parametric ones by (i) using a studentization argument (which leads to what we call pseudo-FvML tests) and by (ii) resorting to the invariance principle (which leads to efficient rank-based tests). Within each construction the semi-parametric tests inherit optimality under a given distribution (the FvML distribution in the first case, any rotationally symmetric distribution in the second) from their parametric antecedents and also improve on the latter by being valid under the whole class of rotationally symmetric distributions. Asymptotic relative efficiencies are calculated and the finite-sample behavior of the proposed tests is investigated by means of a Monte Carlo simulation. We conclude by applying our findings on a real-data example involving geological data.