A Comparative Study of Several Robust Estimates of Slope, Intercept, and Scale in Linear Regression

Abstract

Three classes of M estimates for robust linear regression are investigated for various contaminated normal distributions, sample sizes, and distributions of the independent variable. These are the L_p estimates, the amt estimate, and a new class of estimates (E_a ) with bounded influence function. It is found that the E_a class consistently outperforms the L_p class, performs about as well as the amt estimate, and solutions for E_a estimates can be obtained rapidly and reliably. Results are also reported on a robust scale estimate in the E_a class which has negligible bias for normal distributions.

Key Words:

• M estimates
• Robust estimation of location and scale
• E_a estimates
• Iterative weighted least squares
• Acceleration of implicit equation iterations
• Relative efficiency of M estimates