On optimal block resampling for Gaussian-subordinated long-range dependent processes
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高斯从属长程依赖过程的最优分块重抽样
- 研究问题
- 对平稳长记忆高斯序列的非线性变换，分块重抽样的方差估计性能和最优块长如何受非线性、记忆强度及样本量影响？
- 方法与思路
- 作者研究样本均值方差的分块重抽样估计，并扩展至一般统计泛函；分析非线性与长记忆的作用，提出数据驱动块长规则。
- 材料陈述的贡献
- 摘要称最优块长还取决于超出 Hermite 秩的信息，纠正强依赖必然需要更大块长的直觉，并给出一致的数据驱动选择规则。
- 阅读关注点
- 应核对非线性特征如何进入误差展开、最优块长的分情形表达，以及选择规则的一致性条件与一般统计泛函的扩展范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；摘要未给出各情形的具体条件，不能将某一块长阶数普遍用于长记忆过程。
原文摘要
Block-based resampling estimators have been intensively investigated for weakly dependent time processes, which has helped to inform implementation (e.g., best block sizes). However, little is known about resampling performance and block sizes under strong or long-range dependence. To establish guideposts in block selection, we consider a broad class of strongly dependent time processes, formed by a transformation of a stationary long-memory Gaussian series, and examine block-based resampling estimators for the variance of the prototypical sample mean; extensions to general statistical functionals are also considered. Unlike weak dependence, the properties of resampling estimators under strong dependence are shown to depend intricately on the nature of non-linearity in the time series (beyond Hermite ranks) in addition the long-memory coefficient and block size. Additionally, the intuition has often been that optimal block sizes should be larger under strong dependence (say $O(n^{1/2})$ for a sample size $n$) than the optimal order $O(n^{1/3})$ known under weak dependence. This intuition turns out to be largely incorrect, though a block order $O(n^{1/2})$ may be reasonable (and even optimal) in many cases, owing to non-linearity in a long-memory time series. While optimal block sizes are more complex under long-range dependence compared to short-range, we provide a consistent data-driven rule for block selection, and numerical studies illustrate that the guides for block selection perform well in other block-based problems with long-memory time series, such as distribution estimation and strategies for testing Hermite rank.