Parametric estimation for functional autoregressive processes on the sphere

TL;DR

This paper introduces a nonlinear least squares estimator for spectral parameters of spherical autoregressive processes, analyzing its asymptotic properties like consistency and normality in a parametric framework.

Contribution

It develops a new estimation method for spherical AR(1) processes and studies its asymptotic behavior, advancing spectral analysis on the sphere.

Findings

Estimator is weakly consistent

Estimator is asymptotically normal

Provides theoretical guarantees for spectral parameter estimation

Abstract

The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as weak consistency and asymptotic normality.