Robust linear model selection by cross-validation

doi:10.2307/2965566

Robust linear model selection by cross-validation

1997-09-01

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AI

DOI：10.2307/2965566

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Abstract

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This article gives a robust technique for model selection in regression models, an important aspect of any data analysis involving regression. 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 for 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 prediction. We demonstrate the effectiveness of our robust procedure in providing protection against outliers both in a simulation study and in a real example. We contrast the results with those obtained by Shao's method, demonstrating a substantial improvement in choosing the correct model in the presence of outliers with little loss of efficiency at the normal model.

Keywords:

bounded influence

construction sample

outliers

prediction error

robust prediction

validation sample

Robust linear model selection by cross-validation

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