标题： 关于再抽样方法在长记忆下的有效性 显示英文标题

标题： On the validity of resampling methods under long memory

摘要： 对于长记忆时间序列，基于重采样的推断具有至关重要的意义，因为渐近分布通常是非高斯的，并且难以从统计上确定。然而，由于强依赖性，建立重采样方法的渐近有效性并非易事。本文推导了长记忆时间序列两个有限块之间的典型相关的一个有效界值。我们展示了如何应用这个界值来证明在长记忆下，子采样程序对一般统计量的渐近一致性。它允许子样本大小 $b$ 可以是 $o(n)$，其中 $n$ 是样本大小，与记忆强度无关。这使得我们能够改进文献中的许多结果。我们还考虑了在长记忆下子采样程序应用于样本协方差、M估计和经验过程的应用。 显示英文摘要

摘要： For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic consistency of subsampling procedures for general statistics under long memory. It allows the subsample size $b$ to be $o(n)$, where $n$ is the sample size, irrespective of the strength of the memory. We are then able to improve many results found in the literature. We also consider applications of subsampling procedures under long memory to the sample covariance, M-estimation and empirical processes.