Nonparametric Smoothing of Directional and Axial Data

Lutz Duembgen; Caroline Haslebacher

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arXiv · 2501.17463

Nonparametric Smoothing of Directional and Axial Data

Lutz Duembgen·Caroline Haslebacher

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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.

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Lutz Duembgen, Caroline Haslebacher. 2025-01-29. Nonparametric Smoothing of Directional and Axial Data. https://arxiv.org/abs/2501.17463

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