For datasets with unknown but stationary serial dependence, a robust long run variance estimator is essential to handle diverse scenarios. Spectral variance estimators are commonly used but tend to exhibit significant negative bias in the presence of positive correlation. To overcome this, zero lugsail estimators have been introduced, offering zero asymptotic bias regardless of the correlation structure. However, there are currently no guidelines for selecting the optimal bandwidth for lugsail estimators, a critical component in the estimation process. We propose an inference optimal bandwidth rule for lugsail estimators, based on nonstandard fixed-smoothing limiting distributions developed in our study. This approach significantly improves bias correction, accounts for variability, and provides an estimator optimized for robust inference. Our theoretical findings are supported by a simulation study.

翻译：针对具有未知但平稳序列依赖性的数据集，鲁棒的长期方差估计器对于处理多样场景至关重要。谱方差估计器虽被广泛使用，但在存在正相关时往往表现出显著的负偏倚。为克服此问题，零鲁格尔帆估计器被引入，其能够无论相关结构如何均提供零渐近偏倚。然而，目前尚无指导如何为鲁格尔帆估计器选择最优带宽的原则——而这是估计过程中的关键环节。我们基于本研究推导的非标准固定平滑极限分布，提出了一种适用于鲁格尔帆估计器的推断最优带宽准则。该方法显著改进了偏倚校正，兼顾变异性，并提供了一种针对鲁棒推断优化的估计器。我们的理论发现得到了仿真研究的支持。