Regression Models for Directional Data Based on Nonnegative Trigonometric Sums

TL;DR

This paper introduces regression models for circular data using nonnegative trigonometric sums (NNTS), transforming circular variables into linear ones to apply standard regression techniques, and demonstrates their effectiveness with simulated and real data.

Contribution

It proposes a novel regression approach for circular data based on NNTS models, enabling linear regression methods to be used on transformed circular variables.

Findings

NNTS models can capture skewness and multimodality in circular data.

The proposed regression models perform well on simulated data.

Application to real data shows practical usefulness.

Abstract

The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is the surface of a hypersphere; thus, constructing regression models for a circular-dependent variable using NNTS models can comprise fitting great (small) circles on the parameter hypersphere that can identify different regions (rotations) along the great (small) circle. We propose regression models for circular- (angular-) dependent random variables in which the original circular random variable, which is assumed to be distributed (marginally) as an NNTS model, is transformed into a linear random variable such that common methods for linear regression can be applied. The usefulness of NNTS models with skewness and multimodality is shown in examples with simulated and real data.