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.
Caponera, Alessia; Marinucci, D. (2021). Asymptotics for spherical functional autoregressions. ANNALS OF STATISTICS, (ISSN: 0090-5364), 49:1, 346-369. Doi: 10.1214/20-AOS1959.
Asymptotics for spherical functional autoregressions
Caponera, A;
2021
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.
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