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February 2021 Asymptotics for spherical functional autoregressions
Alessia Caponera, Domenico Marinucci
Ann. Statist. 49(1): 346-369 (February 2021). DOI: 10.1214/20-AOS1959

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.

Citation

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Alessia Caponera. Domenico Marinucci. "Asymptotics for spherical functional autoregressions." Ann. Statist. 49 (1) 346 - 369, February 2021. https://doi.org/10.1214/20-AOS1959

Information

Received: 1 July 2019; Revised: 1 December 2019; Published: February 2021
First available in Project Euclid: 29 January 2021

Digital Object Identifier: 10.1214/20-AOS1959

Subjects:
Primary: 62M15
Secondary: 60F05, 60G15, 62M40

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 1 • February 2021
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