A general framework for circular local likelihood regression

TL;DR

This paper introduces a comprehensive framework for nonparametric estimation of regression models with circular covariates, utilizing circular local likelihood, with theoretical properties and practical applications demonstrated.

Contribution

It develops a general nonparametric approach for circular covariate regression models, including smoothing parameter selection and bias-variance analysis, validated through simulations and real data.

Findings

Estimator is asymptotically normal.

Effective smoothing parameter selection method.

Performs well across various response distributions.

Abstract

This paper 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.