ASYMPTOTICS FOR SPHERICAL FUNCTIONAL AUTOREGRESSIONS

• 成果类型: Article
• 署名作者: Caponera, Alessia; Marinucci, Domenico
• 署名单位: Sapienza University Rome; University of Rome Tor Vergata
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1959
• 发表日期: 2021
• 页码: 346-369
• 关键词: gaussian random-fields; time-series; covariance; REGULARITY

摘要

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.