Adaptive warped kernel estimation for nonparametric regression with circular responses

In this paper, we deal with nonparametric regression for cir- cular 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...

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Bibliographic Details
Published in:Electronic journal of statistics 2023-01, Vol.17 (2), p.4011-4048
Main Authors: Nguyen, Tien Dat, Pham Ngoc, Thanh Mai, Rivoirard, Vincent
Format: Article
Language:English
Subjects:
Mathematics
Statistics
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Summary:In this paper, we deal with nonparametric regression for cir- cular 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 op- timal 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.
ISSN:1935-7524
1935-7524
DOI:10.1214/23-EJS2186