Optimal method in multiple regression with structural changes

TL;DR

This paper develops optimal estimation methods for multiple regression models with unknown change-points, introducing a class of shrinkage estimators that outperform traditional estimators under certain conditions.

Contribution

It proposes a new class of estimators for regression with change-points, generalizes conditions for their dominance, and applies the method to real economic data.

Findings

Shrinkage estimators can outperform unrestricted estimators under specific conditions.

Theoretical derivations of bias and risk functions for shrinkage estimators.

Simulation results support the theoretical advantages of the proposed estimators.

Abstract

In this paper, we consider an estimation problem of the regression coefficients in multiple regression models with several unknown change-points. Under some realistic assumptions, we propose a class of estimators which includes as a special cases shrinkage estimators (SEs) as well as the unrestricted estimator (UE) and the restricted estimator (RE). We also derive a more general condition for the SEs to dominate the UE. To this end, we generalize some identities for the evaluation of the bias and risk functions of shrinkage-type estimators. As illustrative example, our method is applied to the "gross domestic product" data set of 10 countries whose USA, Canada, UK, France and Germany. The simulation results corroborate our theoretical findings.