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

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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 Lp estimates, the amt estimate, and a new class of estimates (Ea ) with bounded influence function. It is found that the Ea class consistently outperforms the Lp class, performs about as well as the amt estimate, and solutions for Ea estimates can be obtained rapidly and reliably. Results are also reported on a robust scale estimate in the Ea class which has negligible bias for normal distributions.

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