Bootstrapping data arrays of arbitrary order

By Art B. Owen, Dean Eckles. 2011

40 citations recorded by the source corpus.

In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each observation the product of independently sampled factor weights. No exact bootstrap exists for this problem [McCullagh (2000) Bernoulli 6 285-301]. We show that the proposed bootstrap is mildly conservative, meaning biased toward overestimating the variance, under sufficient conditions that allow very unbalanced and heteroscedastic inputs. Earlier results for a resampling bootstrap only apply to two factors and use multinomial weights that are poorly suited to online computation. The proposed reweighting approach can be implemented in parallel and online settings. The results for this method apply to any number of factors. The method is illustrated using a 3 factor data set of comment lengths from Facebook.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

Rumor Cascades (2014, methodology): “All statistical inference in this section uses confidence intervals and p-values from an online half-sampling bootstrap (Owen and Eckles 2012) clustered on URL.”
Identity and Opinion: A Randomized Experiment (2014, unknown): “In order to produce credible inferences about our uncertainty for identity eﬀects, we use utilize a recently developed multiway bootstrap procedure (Owen and Eckles 2012), randomly resampling comments and viewers jointly to produce a sequence of model parameter estimates which can be aggregated to…”