Oracle inequalities for multi-fold cross validation

Vaart Aad W. van der, Dudoit Sandrine and Laan Mark J. van der

Statistics & Risk Modeling, 2006, vol. 24, issue 3, 351-371

Abstract: We consider choosing an estimator or model from a given class by cross validation consisting of holding a nonneglible fraction of the observations out as a test set. We derive bounds that show that the risk of the resulting procedure is (up to a constant) smaller than the risk of an oracle plus an error which typically grows logarithmically with the number of estimators in the class. We extend the results to penalized cross validation in order to control unbounded loss functions. Applications include regression with squared and absolute deviation loss and classification under Tsybakov’s condition.

Keywords: model selection; oracle inequality; adaptation (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
https://doi.org/10.1524/stnd.2006.24.3.351 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:24:y:2006:i:3:p:21:n:3

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1524/stnd.2006.24.3.351

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().