The S-Estimator in Change-Point Random Model with Long Memory

TL;DR

This paper investigates the robustness and asymptotic properties of S-estimators in two-phase linear regression models with long-range dependent Gaussian errors and regressors, demonstrating their consistency and convergence rate.

Contribution

It extends the application of S-estimators to models with long memory dependencies, providing theoretical guarantees for their robustness and asymptotic behavior.

Findings

S-estimators are strongly consistent in long-memory models

Convergence rates of S-estimators are established

Outliers do not significantly affect the estimators

Abstract

The paper considers two-phase random design linear regression models. The errors and the regressors are stationary long-range dependent Gaussian. The regression parameters, the scale parameters and the change-point are estimated using a method introduced by Rousseeuw and Yohai(1984). This is called S-estimator and it has the property that is more robust than the classical estimators; the outliers don't spoil the estimation results. Some asymptotic results, including the strong consistency and the convergence rate of the S-estimators, are proved.