Variable Selection in Regression Model with AR(p) Error Terms Based on Heavy Tailed Distributions

TL;DR

This paper develops penalized variable selection methods for regression models with autoregressive error terms under heavy-tailed distributions, addressing limitations of existing methods that assume uncorrelated errors and normality.

Contribution

It introduces a novel approach combining parameter estimation and variable selection in autoregressive error models with heavy-tailed errors, expanding applicability beyond normality assumptions.

Findings

Penalized methods perform well in simulations with heavy-tailed errors.

The approach effectively selects relevant variables in real data.

Simulation and real data examples demonstrate improved estimation accuracy.

Abstract

Parameter estimation and the variable selection are two pioneer issues in regression analysis. While traditional variable selection methods require prior estimation of the model parameters, the penalized methods simultaneously carry on parameter estimation and variable select. Therefore, penalized variable selection methods are of great interest and have been extensively studied in literature. However, most of the papers in literature are only limited to the regression models with uncorrelated error terms and normality assumption. In this study, we combine the parameter estimation and the variable selection in regression models with autoregressive error term by using different penalty functions under heavy tailed error distribution assumption. We conduct a simulation study and a real data example to show the performance of the estimators.