Nonparametric Smoothing of Directional and Axial Data

TL;DR

This paper develops nonparametric smoothing techniques for directional and axial data using generalized linear models with von Mises-Fisher and Bingham distributions, including computational methods and applications to planetary science data.

Contribution

It introduces a local polynomial regression approach for nonparametric smoothing of directional data modeled by von Mises-Fisher and Bingham distributions, with computational parametrization.

Findings

Effective smoothing of directional data demonstrated on simulated datasets.

Application to planetary science data shows practical utility.

Computational methods for Euclidean parametrization of distributions.

Abstract

We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we parametrize von Mises-Fisher distributions by Euclidean parameters and investigate computational aspects of this parametrization. Then we modify this approach for local polynomial regression as a means of nonparametric smoothing of distributional data. The methods are illustrated with simulated data and a data set from planetary sciences involving covariate vectors on a sphere with axial response.