Adaptive warped kernel estimation for nonparametric regression with circular responses

Tien-Dat Nguyen (1) , Thanh Mai Pham Ngoc (1) , Vincent Rivoirard (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: circular data; nonparametric regression; warping method; kernel rule; adaptive minimax estimation; Goldenshluger-Lepski procedure

Domaines: Statistiques [math.ST]

Tien-Dat Nguyen, Thanh Mai Pham Ngoc, Vincent Rivoirard. Adaptive warped kernel estimation for nonparametric regression with circular responses. Electronic Journal of Statistics , 2023, 17 (2), pp.4011-4048. ⟨10.1214/23-EJS2186⟩. ⟨hal-03633917v2⟩