Kernel density estimation for stationary random fields with values in a finite-dimensional Riemannian manifold

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

This paper investigates some asymptotic properties of the kernel spatial density estimation for stationary α-mixing process on a finite-dimensional Riemannian manifold without boundary. The results extend beyond the classical independently and identically distributed (i.i.d.) data, focusing on the case where the manifold is known and extending the classical theory to random fields.

Mots clés: Kernel density estimator Riemannian manifolds Spatial data Mixing condition Random fields Mean Squared Error Convergence in probability; Kernel density estimator; Riemannian manifolds; Spatial data; Mixing condition; Random fields; Mean Squared Error; Convergence in probability

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

Wiem Nefzi, Anne-Françoise Yao, Salah KHARDANI. Kernel density estimation for stationary random fields with values in a finite-dimensional Riemannian manifold. 2025. ⟨hal-04896382⟩