论文标题
时间序列分析中不确定性定量的高阶近似
Higher-order approximation for uncertainty quantification in time series analysis
论文作者
论文摘要
对于具有高时间相关性的时间序列，经验过程的收敛速度相当缓慢地转换为其限制分布。变更点分析，拟合测试和不确定性定量的许多统计数据都将表示为经验过程的功能，因此继承了其缓慢的收敛性。结果，基于这些数量的渐近分布的推论会受到相对较小的样本量的显着影响。我们通过得出相应误差项的渐近分布来评估经验过程的高阶近似值。基于高阶项的限制分布，我们提出了一种新的方法来计算统计量（例如中位数）的置信区间。在一项仿真研究中，我们将这些置信区间的覆盖率和长度与基于经验过程的渐近分布的覆盖率和长度进行了比较，并突出了经验过程的高阶近似值的某些好处。
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a representation as functionals of the empirical process and therefore inherit its slow convergence. As a result, inference based on the asymptotic distribution of those quantities is significantly affected by relatively small sample sizes. We assess the quality of higher-order approximations of the empirical process by deriving the asymptotic distribution of the corresponding error terms. Based on the limiting distribution of the higher-order terms, we propose a novel approach to calculate confidence intervals for statistical quantities such as the median. In a simulation study, we compare coverage rates and lengths of these confidence intervals with those based on the asymptotic distribution of the empirical process and highlight some benefits of higher-order approximations of the empirical process.
