LASSO estimation for spherical autoregressive processes

TL;DR

This paper introduces LASSO estimators for spherical functional autoregressive processes, analyzing their properties such as consistency and oracle inequalities in the spectral domain.

Contribution

It is the first to develop LASSO-based estimation methods for spherical autoregressive kernels using spectral decompositions.

Findings

LASSO estimators are consistent for spherical AR processes.

Oracle inequalities are established for the proposed estimators.

The methods are validated through theoretical analysis.

Abstract

The purpose of the present paper is to investigate on a class of spherical functional autoregressive processes in order to introduce and study LASSO (Least Absolute Shrinkage and Selection Operator) type estimators for the corresponding autoregressive kernels, defined in the harmonic domain by means of their spectral decompositions. Some crucial properties for these estimators are proved, in particular, consistency and oracle inequalities.