ROBUST INFERENCE FOR THE MEAN IN THE PRESENCE OF SERIAL CORRELATION AND HEAVY-TAILED DISTRIBUTIONS
研究了时间序列均值在可能重尾情况下的统计推断问题，提出了无需知道依赖特征或尾指数的自归一化样本均值和置信区间方法，并通过对称化技术构建了兼具稳健性和精度的分布估计量。
The problem of statistical inference for the mean of a time series with possibly heavy tails is considered. We first show that the self-normalized sample mean has a well-defined asymptotic distribution. Subsampling theory is then used to develop asymptotically correct confidence intervals for the mean without knowledge (or explicit estimation) either of the dependence characteristics, or of the tail index. Using a symmetrization technique, we also construct a distribution estimator that combines robustness and accuracy: it is higher-order accurate in the regular case, while remaining consistent in the heavy tailed case. Some finite-sample simulations confirm the practicality of the proposed methods.