A1198
Title: Kernel regression estimation for stochastic process with values in a Riemannian manifold
Authors: Papa Mbaye - University Clermont Auvergne (France)
Mohamed Abdillahi Isman - University Clermont Auvergne (France) [presenting]
Salah Khardani - Universite El Manar - Laboratoire M2AHTP (Tunisia)
Anne Francoise Yao - Universite Clermont Auvergne/LMBP (France)
Wiem Nefzi - Universite El Manar - Laboratoire M2AHTP (Tunisia)
Abstract: The aim is to study the behavior of the kernel regression estimator when the output is a real-valued random variable, Y and the input, X, is a random variable which takes place in a finite-dimensional Riemannian submanifold. The results of a past study are extended to independent identically distributed observations in the case of dependent data under some mixing conditions. Specifically, the rate of convergence is given in mean square error meaning, probability, and almost surely. Furthermore, a central limit theorem is established, and the purpose is illustrated through some simulations and a real data application.
