Nonparametric regression on Riemannian manifolds under an α -mixing process
Abstract
.This article investigates the asymptotic properties of a kernel estimator of the regression function linking a real-valued response Y to a covariate X taking values in a Riemannian submanifold ℳ. The estimator is an adaptation of the non parametric regression estimator introduced by Pelletier (Citation2006) for i.i.d. data on manifolds to the case where the observations (Xt,Yt)t∈Z form a stationary α-mixing process. Under suitable geometric regularity and mixing assumptions, we derive explicit expressions for the bias and the variance of the estimator, obtain the optimal bandwidth that minimizes the mean squared error, and establish the optimal rate of convergence in mean squared error. As a consequence, we prove both pointwise and uniform convergence in probability of the estimator on compact Riemannian manifolds under dependence.
Fields of Study & Subjects
Morphological variations and asymmetry
Bayesian Methods and Mixture Models
advanced mathematical theories
Publication details
- Journal / source
- Communication in Statistics- Theory and Methods
- Publisher
- Informa UK Limited
- Volume
- 55
- Issue
- 15
- Pages
- 5148–5163
- Publication date
- 5 February 2026
- Language
- EN