论文标题
Bootstrap平均值和其他随机加权总和的强大统一定律
Strong uniform laws of large numbers for bootstrap means and other randomly weighted sums
论文作者
论文摘要
本文为随机加权总和（例如bootstrap均值）建立了大量的新颖的强统一定律。通过利用最近的进步，这些结果将其一般适用性的先前工作扩展到了广泛的加权程序，并且相对于有效的自举样本量，它们的灵活性。除了标准的多项式hootstrap和N Bootstrap的标准外，我们的结果还适用于涉及负相关（NOD）重量（包括贝叶斯靴子，jack刀，jack刀，重新采样，无需更换的简单随机取样）的大量随机加权总和，包括贝叶斯靴子，重新采样，重新替换，重新替代，独立体重和多重体重量。权重可以在非规模上分配，甚至可能是负面的。我们的证明技术基于扩展I.I.D.的证明。强大的统一法律，以随机加权的款项采用强大的法律；特别是，我们利用了最近的Marcinkiewicz-Zygmund强律，以提高加权总和。
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of weighting procedures and in their flexibility with respect to the effective bootstrap sample size. In addition to the standard multinomial bootstrap and the m-out-of-n bootstrap, our results apply to a large class of randomly weighted sums involving negatively orthant dependent (NOD) weights, including the Bayesian bootstrap, jackknife, resampling without replacement, simple random sampling with over-replacement, independent weights, and multivariate Gaussian weighting schemes. Weights are permitted to be non-identically distributed and possibly even negative. Our proof technique is based on extending a proof of the i.i.d. strong uniform law of large numbers to employ strong laws for randomly weighted sums; in particular, we exploit a recent Marcinkiewicz--Zygmund strong law for NOD weighted sums.
