论文标题
关于高斯征服的远程依赖性过程的最佳块重新采样
On optimal block resampling for Gaussian-subordinated long-range dependent processes
论文作者
论文摘要
基于块的重新采样估计器已对弱依赖时间过程进行了深入研究，这有助于告知实施（例如，最佳块尺寸）。但是，对于在强或远程依赖性下的重新采样性能和块大小知之甚少。为了在块选择中建立指南柱，我们考虑了一类强烈依赖的时间过程，这些过程是由固定的长信使高斯系列的转换形成的，并检查了基于块的重新采样估计器，以实现原型样本均值的方差；还考虑了一般统计功能的扩展。与弱依赖性不同，在强依赖性下，重采样估计量的性质被证明在时间序列（超越HERMITE等级）中的非线性性质不明显，此外还有长期内存系数和块大小。此外，直觉通常是，在强依赖性（例如样本量$ n $ $ n $的$ o（n^{1/2}）$下，最佳块大小应大于最佳订单$ o（n^{1/3}）$。事实证明，这种直觉在很大程度上是不正确的，尽管在许多情况下，由于长期内存时间序列中的非线性，在许多情况下，块顺序$ o（n^{1/2}）$可能是合理的（甚至是最佳）。尽管与短期相比，在远程依赖性下，最佳块大小更为复杂，但我们为块选择提供了一致的数据驱动规则，数值研究表明，块选择的指南在具有长期内存时间序列的其他基于块的问题中表现良好，例如分布估计和测试Hermite等级的策略。
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.
