Open Access
December 2007 The pigeonhole bootstrap
Art B. Owen
Ann. Appl. Stat. 1(2): 386-411 (December 2007). DOI: 10.1214/07-AOAS122


Recently there has been much interest in data that, in statistical language, may be described as having a large crossed and severely unbalanced random effects structure. Such data sets arise for recommender engines and information retrieval problems. Many large bipartite weighted graphs have this structure too. We would like to assess the stability of algorithms fit to such data. Even for linear statistics, a naive form of bootstrap sampling can be seriously misleading and McCullagh [Bernoulli 6 (2000) 285–301] has shown that no bootstrap method is exact. We show that an alternative bootstrap separately resampling rows and columns of the data matrix satisfies a mean consistency property even in heteroscedastic crossed unbalanced random effects models. This alternative does not require the user to fit a crossed random effects model to the data.


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Art B. Owen. "The pigeonhole bootstrap." Ann. Appl. Stat. 1 (2) 386 - 411, December 2007.


Published: December 2007
First available in Project Euclid: 30 November 2007

zbMATH: 1126.62027
MathSciNet: MR2415741
Digital Object Identifier: 10.1214/07-AOAS122

Keywords: Collaborative filtering , recommenders , Resampling

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.1 • No. 2 • December 2007
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