Testing a parametric circular regression function with spatially correlated data

A. Meilán Vila, M. Francisco Fernandez, R. M. Crujeiras Casais

This work proposes new approaches for testing a parametric regression function in linear-circular regression models (with a circular response and Euclidean covariates) featuring spatially correlated errors. The test statistics used in these procedures are based on a comparison between a (non-smoothed or smoothed) parametric fit under the null hypothesis and a nonparametric estimator of the circular regression function. In this framework, a suitable measure of circular distance must be employed. The null hypothesis that the regression function belongs to a certain parametric family is rejected if the distance between the two fits exceeds a certain threshold. Parametric estimation is performed using procedures based on least squares or maximum likelihood. For the nonparametric alternative, a local linear-type estimator is considered. Different bootstrap methods are designed for practical applications, and their performance is analyzed and compared through empirical experiments.

Keywords: circular data, spatial dependence, local linear regression, bootstrap

Nonparametric Statistics: Nonparametric Test
June 13, 2025  11:00 AM
MR 1

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