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, A., Marinucci, D. (2021). Asymptotics for spherical functional autoregressions. ANNALS OF STATISTICS, 49(1), 346-369 [10.1214/20-AOS1959].

Asymptotics for spherical functional autoregressions

Marinucci, D
2021-01-01

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.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
Spherical functional autoregressions
spherical harmonics
quantitative central limit theorem
Wasserstein distance
weak convergence
Caponera, A., Marinucci, D. (2021). Asymptotics for spherical functional autoregressions. ANNALS OF STATISTICS, 49(1), 346-369 [10.1214/20-AOS1959].
Caponera, A; Marinucci, D
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/302563
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