HIGHER-ORDER APPROXIMATION FOR UNCERTAINTY QUANTIFICATION IN TIME-SERIES ANALYSIS
针对时间序列中经验过程收敛慢的问题，推导了高阶近似的误差项渐近分布，并据此提出计算中位数等统计量置信区间的新方法，模拟显示其覆盖率和区间长度优于传统渐近方法。
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 (HOAs) 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 HOAs of the empirical process.