Nonparametric estimation for stationary and strongly mixing processes on Riemannian manifolds

In this paper, nonparametric estimation for a stationary strongly mixing and manifoldvalued process (X-j) is considered. In this non-Euclidean and not necessarily i.i.d setting, we propose kernel density estimators of the joint probability density function, of the conditional probability density functions and of the conditional expectations of functionals of X-j given the past behavior of the process. We prove the strong consistency of these estimators under sufficient conditions, and we illustrate their performance through simulation studies and real data analysis.

Automated summary

This paper considers nonparametric estimation for a stationary strongly mixing and manifold-valued process (X-j), proposing kernel density estimators for the joint probability density function, conditional probability density functions, and conditional expectations of functionals of X-j given the past behavior of the process in a non-Euclidean and not necessarily i.i.d setting. Strong consistency of these estimators is demonstrated under sufficient conditions, with their performance evaluated through simulation studies and real data analysis.