Nonparametric Regression on Riemannian manifold under α-Mixing process

Wiem Nefzi (1, 2) , Anne-Françoise Yao (3, 4, 5) , Salah KHARDANI (6, 2)

1 University of Tunis - Faculty of Sciences of Tunis
2 M2SAS - Laboratoire de Modélisation mathématique, Statistique et Analyse stochastique
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 UCA - Université Clermont Auvergne
5 CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique
6 University of Tunis - Faculty of Sciences of Tunis

The main focus of our paper is to investigate the behavior of the kernel estimator for the regression function between a real-valued random variable Y and a random variable X, where X takes values in a Riemannian submanifold. The estimator is adapted from the article of Pelletier (2006). Additionally, we study data that adheres to the α-mixing condition, which imposes valuable constraints on the dependence structure of the observations. Specifically, we provide the rate of convergence in mean square error, enabling us to assess the precision and efficiency of the estimator.

Mots clés: Non-parametric regression estimator; Kernel method; Riemannian manifolds; Mixing condition

Domaines: Mathématiques [math]; Statistiques [math.ST]; Statistiques [stat]

Wiem Nefzi, Anne-Françoise Yao, Salah KHARDANI. Nonparametric Regression on Riemannian manifold under α-Mixing process. 2025. ⟨hal-04896373⟩