Bounded-Influence Regression via Local Minimax Mean Squared Error

Abstract

The class of “general” M -estimators for the stochastic linear regression model is considered, and influence and change-of-variance functions are used to approximate the main term of the mean squared error (MSE). The estimator is then found in the class that minimizes the maximum of that approximate MSE over the ϵ-contamination neighborhood. This approach allows for additional flexibility of designing estimators optimal for prediction in specific regions of the factor space, and it provides a practical way of choosing estimators' tuning constants as functions of a fraction of contamination and sample size.