Consistency of a hybrid block bootstrap for distribution and variance estimation for sample quantiles of weakly dependent sequences
Consistency of a hybrid block bootstrap for distribution and variance estimation for sample quantiles of weakly dependent sequences
复制标题
用于弱相关序列样本分位数分布和方差估计的混合块引导程序的一致性
DOI：
10.1111/anzs.12206
复制
发表时间：
2018
影响因子：
1.1
通讯作者：
G. A. Young
中科院分区：
文献类型：
--
作者：
Todd A. Kuffner;Stephen M. S. Lee;G. A. Young
Hall、Horowitz 和 Jing ( ) 等人已经彻底研究了用于依赖数据的平滑函数的分布和方差估计的块引导方案的一致性和最优性。然而，对于非光滑泛函（例如分位数），人们所知甚少。 Sun 和 Lahiri ( ) 提出的现有结果，关于通过移动块引导 (MBB) 进行分布和方差估计的强一致性，要求 b→∞，其中 b=⌊n/ℓ⌋ 是要粘贴在一起形成引导数据系列的重采样块的数量，n 是可用样本大小，ℓ 是块长度。在这里我们证明，事实上，弱一致性对于任何 b 都成立，使得 1≤b=O(n/ℓ)。换句话说，我们表明子采样引导 (b=1) 和 MBB 之间的混合是一致的。经验结果说明了混合块引导估计器对于不同数量的块的性能。
Consistency and optimality of block bootstrap schemes for distribution and variance estimation of smooth functionals of dependent data have been thoroughly investigated by Hall, Horowitz & Jing ( ), among others. However, for nonsmooth functionals, such as quantiles, much less is known. Existing results, due to Sun & Lahiri ( ), regarding strong consistency for distribution and variance estimation via the moving block bootstrap (MBB) require that b→∞, where b=⌊n/ℓ⌋ is the number of resampled blocks to be pasted together to form the bootstrap data series, n is the available sample size, and ℓ is the block length. Here we show that, in fact, weak consistency holds for any b such that 1≤b=O(n/ℓ). In other words we show that a hybrid between the subsampling bootstrap (b=1) and MBB is consistent. Empirical results illustrate the performance of hybrid block bootstrap estimators for varying numbers of blocks.