Nonparametric tests for circular regression

TL;DR

This paper introduces nonparametric kernel-based methods for testing effects and comparing regression curves in models with circular variables, addressing key issues in circular regression analysis.

Contribution

It proposes flexible kernel regression-based tests for no-effect, equality, and parallelism in circular regression models, with demonstrated finite sample performance.

Findings

Methods perform well in simulations

Effective in real data examples

Flexible approach for circular regression analysis

Abstract

No matter the nature of the response and/or explanatory variables in a regression model, some basic issues such as the existence of an effect of the predictor on the response, or the assessment of a common shape across groups of observations, must be solved prior to model fitting. This is also the case for regression models involving circular variables (supported on the unit circumference). In that context, using kernel regression methods, this paper provides a flexible alternative for constructing pilot estimators that allow to construct suitable statistics to perform no-effect tests and tests for equality and parallelism of regression curves. Finite sample performance of the proposed methods is analyzed in a simulation study and illustrated with real data examples.