Adaptive estimation for nonparametric circular regression with errors in variables

TL;DR

This paper develops adaptive nonparametric estimators for circular regression with measurement errors, analyzing their theoretical properties and demonstrating practical effectiveness through simulations and real data applications.

Contribution

It introduces novel adaptive estimators for circular regression with errors-in-variables, applicable to both circular and linear covariates, with proven convergence rates.

Findings

Estimators achieve optimal convergence rates over Sobolev and H"older classes.

Numerical experiments confirm the estimators' practical performance.

Method effectively handles errors in both circular and linear covariates.

Abstract

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are constructed and their theoretical performance is assessed through convergence rates over Sobolev and H\"older smoothness classes. Numerical experiments on simulated and real datasets illustrate the practical relevance of the methodology.