Open Access
2023 Adaptive warped kernel estimation for nonparametric regression with circular responses
Tien Dat Nguyen, Thanh Mai Pham Ngoc, Vincent Rivoirard
Author Affiliations +
Electron. J. Statist. 17(2): 4011-4048 (2023). DOI: 10.1214/23-EJS2186


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 Hölder 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.

Funding Statement

T.D.N. was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.


The authors would like to warmly thank the Associate Editor and the anonymous referees for very valuable comments and suggestions. Parts of this work were conducted during T.D.N.’s PhD study at Laboratoire de Mathématiques d’Orsay, UMR 8628, Université Paris-Saclay, 91405 Orsay, France.


Download Citation

Tien Dat Nguyen. Thanh Mai Pham Ngoc. Vincent Rivoirard. "Adaptive warped kernel estimation for nonparametric regression with circular responses." Electron. J. Statist. 17 (2) 4011 - 4048, 2023.


Received: 1 April 2022; Published: 2023
First available in Project Euclid: 20 December 2023

Digital Object Identifier: 10.1214/23-EJS2186

Primary: 62G08 , 62H11

Keywords: adaptive minimax estimation , Circular data , Goldenshluger-Lepski procedure , kernel rule , Nonparametric regression , warping method

Vol.17 • No. 2 • 2023
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