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The pigeonhole bootstrap. (English) Zbl 1126.62027

Summary: 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 P. McCullagh [Bernoulli 6, 285–301 (2000; Zbl 0976.62035)] 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.

MSC:

62G09 Nonparametric statistical resampling methods
62P99 Applications of statistics

Citations:

Zbl 0976.62035
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References:

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