ROBUST LINEAR-MODEL SELECTION BY CROSS-VALIDATION

This article gives a robust technique for model selection in regressio n models, an important aspect of any data analysis involving regressio n. There is a danger that outliers will have an undue influence on the model chosen and distort any subsequent analysis. We provide a robust algorithm for model selection using Shao's cross-validation methods f or choice of variables as a starting point. Because Shao's techniques are based on least squares, they are sensitive to outliers. We develop our robust procedure using the same ideas of cross-validation as Shao but using estimators that are optimal bounded influence for predictio n. We demonstrate the effectiveness of our robust procedure in providi ng protection against outliers both in a simulation study and in a rea l example. We contrast the results with those obtained by Shao's metho d, demonstrating a substantial improvement in choosing the correct mod el in the presence of outliers with little loss of efficiency at the n ormal model.