Nonparametric regression for a circular response with error-in-covariate

TL;DR

This paper develops three nonparametric estimators for circular regression with measurement error in covariates, introducing a new bandwidth selection method and analyzing their theoretical and empirical performance.

Contribution

It proposes three novel estimators for circular regression with error-in-covariate, linked through deconvolution, and introduces an efficient bandwidth selection technique.

Findings

Estimators have desirable asymptotic properties.

New bandwidth method improves computational efficiency.

Empirical results demonstrate estimator effectiveness.

Abstract

This study considers regression analysis of a circular response with an error-prone linear covariate. Starting with an existing estimator of the circular regression function that assumes error-free covariate, three approaches are proposed to revise this estimator, leading to three nonparametric estimators for the circular regression function accounting for measurement error. The proposed estimators are intrinsically connected through some deconvoluting operator that is exploited differently in different estimators. Moreover, a new bandwidth selection method is developed that is more computationally efficient than an existing method well-received in the context of tuning parameter selection in the presence of measurement error. The efficacy of these new estimators and their relative strengths are demonstrated through a thorough investigation of their asymptotic properties and extensive empirical study of their finite-sample performance.