Open Access
December 2007 Consistency of cross validation for comparing regression procedures
Yuhong Yang
Ann. Statist. 35(6): 2450-2473 (December 2007). DOI: 10.1214/009053607000000514


Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for kernel smoothing). However, little is known about consistency of cross validation when applied to compare between parametric and nonparametric methods or within nonparametric methods. We show that under some conditions, with an appropriate choice of data splitting ratio, cross validation is consistent in the sense of selecting the better procedure with probability approaching 1.

Our results reveal interesting behavior of cross validation. When comparing two models (procedures) converging at the same nonparametric rate, in contrast to the parametric case, it turns out that the proportion of data used for evaluation in CV does not need to be dominating in size. Furthermore, it can even be of a smaller order than the proportion for estimation while not affecting the consistency property.


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Yuhong Yang. "Consistency of cross validation for comparing regression procedures." Ann. Statist. 35 (6) 2450 - 2473, December 2007.


Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1129.62039
MathSciNet: MR2382654
Digital Object Identifier: 10.1214/009053607000000514

Primary: 62B10 , 62G07
Secondary: 62C20

Keywords: consistency , Cross validation , Model selection

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • December 2007
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