Bootstrapping data arrays of arbitrary order
نویسندگان
چکیده
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 its factor weights. No exact bootstrap exists for this problem (McCullagh, 2000). We show that the proposed bootstrap is mildly conservative, under sufficient conditions that allow very unbalanced and heteroscedastic inputs. Earlier results for a resampling bootstrap only apply to two factors and are not suitable 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.
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