Goodness-of-fit tests for parametric regression models with circular response

TL;DR

This paper introduces new goodness-of-fit tests for parametric regression models with circular responses, applicable to both independent and spatially correlated data, using bootstrap calibration and simulation validation.

Contribution

It proposes novel test statistics based on circular distances and develops bootstrap methods for calibration, addressing both independent and spatially correlated data scenarios.

Findings

Tests perform well in finite samples across various scenarios.

Bootstrap procedures effectively calibrate the tests.

Method applicable to both independent and spatially correlated data.

Abstract

Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are based on a circular distance comparing a (non-smoothed or smoothed) parametric circular estimator and a nonparametric one. Properly designed bootstrap procedures for calibrating the tests in practice are also presented. Finite sample performance of the tests in different scenarios with independent and spatially correlated samples, is analyzed by simulations.