In this paper, we investigate a class of spherical functional autoregressive processes, and we discuss the estimation of the corresponding autoregressive kernels. In particular, we first establish a consistency result (in mean-square and sup norm), then a quantitative central limit theorem (in Wasserstein distance), and finally a weak convergence result, under more restrictive regularity conditions. Our results are validated by a small numerical investigation.
"Asymptotics for spherical functional autoregressions." Ann. Statist. 49 (1) 346 - 369, February 2021. https://doi.org/10.1214/20-AOS1959