Robust Estimation of Multivariate Linear Model Based on Depth Weighted Mean and Scatter

Abstract

Based on the projection depth weighted mean and scatter estimation of the joint distribution of (x, y), we introduce a robust estimator of the regression coefficients for the multivariate linear model. The new estimator possesses desirable properties including affine invariance, Fisher consistency, and asymptotic normality. Also, we study the robustness of the estimator in terms of breakdown point and influence function. Extensive simulation studies are performed to investigate the finite sample behavior of robustness and efficiency. The methodology is illustrated with a real data example.

Keywords:

• Breakdown point
• Depth
• Influence function
• Multivariate regression
• Robust estimation
• Scatter estimator

Mathematics Subject Classification:

• 62J05
• 62H12
• 62G35