Conditional Maximum Lq-Likelihood Estimation for Regression Model with Autoregressive Error Terms

TL;DR

This paper introduces a robust parameter estimation method for regression models with autoregressive error terms using Maximum Lq-likelihood, demonstrating improved performance over traditional methods in the presence of outliers.

Contribution

It develops and analyzes a new MLq estimation approach for AR(p) error models, providing asymptotic properties and empirical evidence of robustness.

Findings

MLq estimators outperform ML estimators with outliers

Simulation studies confirm robustness of MLq estimators

Real data example illustrates practical advantages

Abstract

In this article, we consider the parameter estimation of regression model with pth order autoregressive (AR(p)) error term. We use the Maximum Lq-likelihood (MLq) estimation method that is proposed by Ferrari and Yang (2010a), as a robust alternative to the classical maximum likelihood (ML) estimation method to handle the outliers in the data. After exploring the MLq estimators for the parameters of interest, we provide some asymptotic properties of the resulting MLq estimators. We give a simulation study and a real data example to illustrate the performance of the new estimators over the ML estimators and observe that the MLq estimators have superiority over the ML estimators when outliers are present in the data.