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Biometrika Advance Access originally published online on February 28, 2007
Biometrika 2007 94(1):217-229; doi:10.1093/biomet/asm008
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Copyright © 2007 Biometrika Trust

Articles

Variable selection for the single-index model

Efang Kong and Yingcun Xia

Department of Statistics and Applied Probability, National University of Singapore, 117546, Singapore

g0201815{at}nus.edu.sg

staxyc{at}stat.nus.edu.sg

Received for publication 1 August 2005. Revision received 1 June 2006.
  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.

Key Words: consistency • crossvalidation • nonparametric smoothing • semiparametric model • variable selection


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