  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.
