Variable selection for the single‐index model

Efang Kong and Yingcun Xia

Biometrika, 2007, vol. 94, issue 1, 217-229

Abstract: We consider variable selection in the single-index model. We prove that the popular leave-m-out crossvalidation method has different behaviour in the single-index model from that in linear regression models or nonparametric regression models. A new consistent variable selection method, called separated crossvalidation, is proposed. Further analysis suggests that the method has better finite-sample performance and is computationally easier than leave-m-out crossvalidation. Separated crossvalidation, applied to the Swiss banknotes data and the ozone concentration data, leads to single-index models with selected variables that have better prediction capability than models based on all the covariates. Copyright 2007, Oxford University Press.

Date: 2007
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