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Adaptive warped kernel estimation for nonparametric regression with circular responses

Nguyen, Tien-Dat; Pham Ngoc, Thanh Mai; Rivoirard, Vincent (2022), Adaptive warped kernel estimation for nonparametric regression with circular responses. https://basepub.dauphine.psl.eu/handle/123456789/23363

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
25
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Author(s)
Nguyen, Tien-Dat
Laboratoire de Mathématiques d'Orsay [LMO]
Pham Ngoc, Thanh Mai
Laboratoire de Mathématiques d'Orsay [LMO]
Rivoirard, Vincent
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
circular data; nonparametric regression; warping method; kernel rule; adaptive minimax estimation; Goldenshluger-Lepski procedure