Robust Multivariate Regression Based on Shrinkage Sn Estimator

Abstract

The primary goal of multivariate regression analysis is to estimate model parameters. However, when the data includes outliers or extreme observations, the maximum likelihood estimator may not be suitable for estimation. Therefore, it's essential to identify a parameter estimation method that remains relatively unaffected by minor changes in the data. In this paper, we present a robust approach to multivariate regression that relies on the robust estimation of the joint location and scatter matrix for both the explanatory and response variables. We make use shrinkage based robust location and scatter matrix proposed by Lakshmi and Sajesh (2024). Through simulations, we explore the finite-sample performance and robustness of the estimator. To improve efficiency, we suggest a reweighted estimator selected from multiple reweighting options. We demonstrate that the multivariate regression estimator possesses the equivariance properties. The proposed estimator achieves a balance of high robustness and efficiency in estimation. Proposed estimator's efficacy is illustrated using no: of benchmark dataset.