Using the bootstrap to quantify the authority of an empirical ranking
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利用 Bootstrap 量化经验排名的可信程度
- 研究问题
- 对机构表现或基因影响等经验排名，常规 bootstrap 能否可靠刻画名次分布和区间，以及如何修正其失效？
- 方法与思路
- 作者分析常规 bootstrap 的收敛与区间长度，讨论较小重抽样规模的方案及其调参，并比较同步和独立分量重抽样。
- 材料陈述的贡献
- 摘要称常规方案可能不一致，区间长度仅抓住数量级；较小规模重抽样可改善一致性，独立分量方案可缓解部分误导。
- 阅读关注点
- 核对名次差距、维数和依赖结构的条件，区分分布收敛与概率收敛，并检查重抽样规模选择及区间目标。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；各修正方案的充分条件未列出，不能据此认为忽略分量依赖通常有效。
原文摘要
The bootstrap is a popular and convenient method for quantifying the authority of an empirical ordering of attributes, for example of a ranking of the performance of institutions or of the influence of genes on a response variable. In the first of these examples, the number, p, of quantities being ordered is sometimes only moderate in size; in the second it can be very large, often much greater than sample size. However, we show that in both types of problem the conventional bootstrap can produce inconsistency. Moreover, the standard n-out-of-n bootstrap estimator of the distribution of an empirical rank may not converge in the usual sense; the estimator may converge in distribution, but not in probability. Nevertheless, in many cases the bootstrap correctly identifies the support of the asymptotic distribution of ranks. In some contemporary problems, bootstrap prediction intervals for ranks are particularly long, and in this context, we also quantify the accuracy of bootstrap methods, showing that the standard bootstrap gets the order of magnitude of the interval right, but not the constant multiplier of interval length. The m-out-of-n bootstrap can improve performance and produce statistical consistency, but it requires empirical choice of m; we suggest a tuning solution to this problem. We show that in genomic examples, where it might be expected that the standard, “synchronous” bootstrap will successfully accommodate nonindependence of vector components, that approach can produce misleading results. An “independent component” bootstrap can overcome these difficulties, even in cases where components are not strictly independent.