Asymptotics for spherical functional autoregressions
Alessia Caponera, Domenico Marinucci
The Annals of Statistics · 2021 · Volume 49 · Issue 1
Abstract
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.
Keywords
60F05, 60G15, 62M15, 62M40, Quantitative Central Limit Theorem, Spherical functional autoregressions, Spherical harmonics, Wasserstein distance, weak convergence
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