Functional delta-method for the bootstrap of quasi-Hadamard differentiable functionals
Functional delta-method for the bootstrap of quasi-Hadamard differentiable functionals
复制标题
用于引导拟哈达玛可微泛函的泛函 delta 方法
DOI：
10.1214/16-ejs1140
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Henryk Zahle
中科院分区：
文献类型：
--
作者：
E. Beutner;Henryk Zahle
函数δ方法提供了一种方便的工具，用于从相应经验过程的渐近分布导出统计泛函的插入式估计量的渐近分布。此外，它提供了一个工具，从经验过程的自举一致性导出插件估计的自举一致性。最近的研究表明，采用拟Hadamard可微性的概念，可以大大地扩大渐近分布的泛函δ方法的应用范围。在这里，我们在一般情况下表明，这种扩大进行的自举。也就是说，对于拟阿达玛可微泛函，插入式估计量的自举一致性来自相应经验过程的自举一致性。这种扩大往往需要自举经验过程的分布收敛。一个非均匀的超范数后者并不成问题，这将通过实例加以说明。
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a tool to derive bootstrap consistency for plug-in estimators from bootstrap consistency of empirical processes. It has recently been shown that the range of applications of the functional delta-method for the asymptotic distribution can be considerably enlarged by employing the notion of quasi-Hadamard differentiability. Here we show in a general setting that this enlargement carries over to the bootstrap. That is, for quasi-Hadamard differentiable functionals bootstrap consistency of the plug-in estimator follows from bootstrap consistency of the respective empirical process. This enlargement often requires convergence in distribution of the bootstrapped empirical process w.r.t.\ a nonuniform sup-norm. The latter is not problematic as will be illustrated by means of examples.