A nonstandard empirical likelihood for time series
针对标准分块经验似然需指定块长且影响覆盖精度的问题，提出一种使用所有可能数据块长度的新方法，避免块长选择，具有更好的覆盖性能，其极限分布可通过模拟获得。
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 nonstandard, data-blocking rule which uses a data block of every possible length. Consequently, the method does not involve the usual block selection issues and is also anticipated to exhibit better coverage performance. Its nonstandard blocking scheme, however, induces nonstandard 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.