英文文献：A Non-standard Empirical Likelihood for Time Series-时间序列的非标准经验似然
英文文献作者：Daniel J. Nordman,Helle Bunzel,Soumendra N. Lahiri
英文文献摘要：
Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though non-standard, data-blocking rule which uses a data block of every possible length. Consequently, the method involves no block selection and is also anticipated to exhibit better coverage performance. Its non-standard blocking scheme, however, induces non-standard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi-square one, but is distribution-free and can be reproduced through straightforward simulations. Numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard BEL.

平稳、弱依赖时间序列的标准块经验似然(BEL)要求指定固定块长度作为设置置信区域的调优参数。这方面很困难，并且会影响覆盖率的准确性。作为一种替代方案，本文提出了一种基于简单但非标准的数据阻塞规则的新版本BEL，该规则使用了每一个可能长度的数据块。因此，该方法不涉及块选择，也被期望表现出更好的覆盖性能。然而，它的非标准分块方案引出了非标准渐近，与标准BEL相比需要一个显著不同的发展。我们从新的BEL方法中建立对数比统计量的大样本分布，用于校准时间序列的平均或平滑函数参数的置信区域。这个极限定律不是通常的卡方定律，而是无分布的，可以通过直接的模拟来重现。数值研究表明，该方法比标准BEL具有更好的覆盖精度。