Adaptive warped kernel estimation for nonparametric regression with circular responses

TL;DR

This paper introduces a data-driven kernel estimation method for nonparametric regression with circular responses, employing a warping strategy and Goldenshluger-Lepski estimator to achieve near-optimal performance.

Contribution

It develops a novel adaptive kernel estimation technique for circular data using warping and bandwidth selection, with proven near-minimax optimality.

Findings

Method achieves near-optimal rates in minimax sense.

Numerical results demonstrate strong practical performance.

Approach effectively handles the circular nature of responses.

Abstract

In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth parameter. For this purpose, we use a warping strategy combined with a Goldenshluger-Lepski type estimator. To study optimality of our methodology, we consider the minimax setting and prove, by establishing upper and lower bounds, that our procedure is nearly optimal on anisotropic Holder classes of functions for pointwise estimation. The obtained rates also reveal the specific nature of regression for circular responses. Finally, a numerical study is conducted, illustrating the good performances of our approach.