引导任意阶的数据数组
Bootstrapping data arrays of arbitrary order
摘要：
本文研究了多因子交叉随机效应数据集均值方差估计的自举策略。我们独立地对每个因子的水平应用自举重新加权，为每个观察提供独立采样因子权重的乘积。对于这个问题，不存在精确的引导[McCullagh（2000）Bernoulli 6 285-301]。我们表明，建议的自助是温和的保守，这意味着偏向高估方差，在充分的条件下，允许非常不平衡和异方差的输入。早期的结果，resculturebootstrap只适用于两个因素，并使用多项式权重，不适合在线计算。所提出的重新加权方法可以在并行和在线设置中实现。这种方法的结果适用于任何数量的因素。该方法使用来自Facebook的评论长度的3因素数据集来说明。
英文摘要：
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.
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