ASYMPTOTICS FOR SPHERICAL FUNCTIONAL AUTOREGRESSIONS

被引：7

作者：

Caponera, Alessia ^{[1
]}

Marinucci, Domenico ^{[2
]}

机构：

[1] Sapienza Univ Rome, Dept Stat Sci, Rome, Italy

[2] Univ Roma Tor Vergata, Dept Math, Rome, Italy

来源：

ANNALS OF STATISTICS | 2021年 / 49卷 / 01期

关键词：

Spherical functional autoregressions; spherical harmonics; quantitative central limit theorem; Wasserstein distance; weak convergence; GAUSSIAN RANDOM-FIELDS; TIME-SERIES; COVARIANCE; REGULARITY;

D O I：

10.1214/20-AOS1959

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：346 / 369

页数：24

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