A General Framework for Circular Local Likelihood Regression

Abstract

This article presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of a conditional characteristic is carried out nonparametrically, by maximizing the circular local likelihood, and the estimator is shown to be asymptotically normal. The problem of selecting the smoothing parameter is also addressed, as well as bias and variance computation. The performance of the estimation method in practice is studied through an extensive simulation study, where we cover the cases of Gaussian, Bernoulli, Poisson, and Gamma distributed responses. The generality of our approach is illustrated with several real-data examples from different fields. Supplementary materials for this article are available online.

KEYWORDS:

• Circular data
• Data-driven smoothing selection
• Local likelihood
• Nonparametric regression

Supplementary Materials

Supplementary proofs and simulation resultsDocument containing technical proofs and complementary simulation results (PDF file).

Code and datasetsR scripts with code and workflow and data files (folder).

Acknowledgments

The authors thank the Associate Editor and three anonymous reviewers for their helpful comments, which considerably improved the quality of the paper.

Disclosure Statement

The authors report there are no competing interests to declare

Additional information

Funding

M. Alonso-Pena and R.M. Crujeiras acknowledge the support from project PID2020-116587GB-I00, funded by MCIN/AEI/10.13039/501100011033 and the Competitive Reference Groups 2021-2024 (ED431C 2021/24) from the Xunta de Galicia. M. Alonso-Pena and I. Gijbels gratefully acknowledge support from project C16/20/002 of the Research Fund KU Leuven, Belgium. This work was completed while the first author was visiting the Department of Mathematics, KU Leuven, supported by the Xunta de Galicia through the grant ED481A-2019/139 from the Consellería de Educación, Universidade e Formación Profesional. The authors also acknowledge the Supercomputing Center of Galicia (CESGA) for the computational resources.