发表机构
Mofid Securities（Mofid证券）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多元分布拟合检验中 Rosenblatt 变换对坐标排序敏感的问题，提出订单随机化与依赖稳健合并规则，结合双侧统计量和重估计参数自助法，实现校准功效提升，并在外汇风险模型中成功检测出 Brexit 和 COVID 等事件。
AI 中文摘要
我们检验多元向量 X 是否符合指定分布 F，这是 copula 建模和密度预测中的一个问题。Rosenblatt 变换将其简化为均匀性检验，但依赖于任意坐标排序，该排序在依赖关系下强烈影响功效。我们研究订单随机化：在多个随机排序下应用变换，并使用对依赖关系稳健的规则合并证据。重新排序保留了总 Mahalanobis 信号能量，仅重新分配，因此一个排序是幸运或不幸的抽取。在模拟中，我们观察到相对于预期的单一随机排序和顺序不变参考，校准功效有显著提升。两个要素至关重要：一个双侧基础统计量，以及一个重新估计的参数自助法，它在估计的零假设下恢复水平并释放增益。校准的合并检验对偏离形状具有稳健性；我们比较的所有顺序不变参考都不稳健：对称根检验在分散偏离上崩溃，而形状平坦的卡方检验在集中偏离上落后。我们将其应用于一个高斯外汇风险模型，涵盖九种货币的十年每日数据，检测到诸如英国脱欧和 COVID 等事件。虽然我们专注于高斯零假设，但该程序扩展到任何条件分布可计算和可模拟的零假设。
英文摘要
We test whether a multivariate vector X conforms to a specified distribution F, a problem in copula modelling and density forecasting. The Rosenblatt transform reduces it to a test of uniformity, but depends on an arbitrary coordinate ordering that strongly affects power under dependence. We study order randomization: applying the transform under many random orderings and merging the evidence with dependence-robust rules. Reordering conserves the total Mahalanobis signal energy and merely redistributes it, so one ordering is a lucky or unlucky draw. In simulations we observe significant gains in calibrated power over both the expected single random ordering and order-invariant references. Two ingredients are essential: a two-sided base statistic, and a re-estimating parametric bootstrap that restores level under an estimated null and unlocks the gain. The calibrated pooled tests are robust to the departure's shape; no order-invariant reference we compare is: the symmetric-root test collapses on diffuse departures, while the shape-flat chi-squared test trails on concentrated ones. We apply it to a Gaussian foreign-exchange risk model over a decade of daily data on nine currencies, where it detects episodes such as Brexit and COVID. Though we focus on Gaussian nulls, the procedure extends to any null whose conditional distributions can be computed and simulated from.
