Mehrdad Pournaderi
arXiv 27 Sep 2026 · Statistics — Methodology
arXiv:2609.37477 · PDF · Extracted main text
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.
appendix boundary found by appendix_command · 98% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | F. X. Diebold, T. A. Gunther, A. S. Tay, Evaluating density forecast… (1998) https://doi.org/10.2307/2527342 doi:10.2307/2527342 | 1.000 | 5 | 3 | 100% |
| 2 | A. Marandon, L. Lei, D. Mary, E. Roquain, Adaptive novelty detection… (2024) https://doi.org/10.1214/23-AOS2338 doi:10.1214/23-AOS2338 | 1.000 | 5 | 3 | 100% |
| 3 | J. Dovern, H. Manner, Order-invariant tests for proper calibration o… (2020) https://doi.org/10.1002/jae.2755 doi:10.1002/jae.2755 | 0.928 | 4 | 4 | 100% |
| 4 | S. Bates, E. Candès, L. Lei, Y. Romano, M. Sesia, Testing for outlie… (2023) https://doi.org/10.1214/22-AOS2244 doi:10.1214/22-AOS2244 | 0.928 | 4 | 3 | 100% |
| 5 | V. Vovk, R. Wang, Combining $p$-values via averaging, Biometrika 107… (2020) https://doi.org/10.1093/biomet/asaa027 doi:10.1093/biomet/asaa027 | 0.737 | 3 | 2 | 100% |
| 6 | C. Genest, B. Rémillard, D. Beaudoin, Goodness-of-fit tests for copu… (2009) https://doi.org/10.1016/j.insmatheco.2007.10.005 doi:10.1016/j.insmatheco.2007.10.005 | 0.644 | 2 | 2 | 100% |
| 7 | P. Grünwald, R. de Heide, W. Koolen, Safe testing, Journal of the Ro… (2024) https://doi.org/10.1093/jrsssb/qkae011 doi:10.1093/jrsssb/qkae011 | 0.644 | 2 | 2 | 100% |
| 8 | R. J. Simes, An improved Bonferroni procedure for multiple tests of… (1986) https://doi.org/10.1093/biomet/73.3.751 doi:10.1093/biomet/73.3.751 | 0.644 | 2 | 2 | 100% |
| 9 | V. Vovk, R. Wang, E-values: Calibration, combination and application… (2021) https://doi.org/10.1214/20-AOS2020 doi:10.1214/20-AOS2020 | 0.644 | 2 | 2 | 100% |
| 10 | R. Wang, A. Ramdas, False discovery rate control with e-values, Jour… (2022) https://doi.org/10.1111/rssb.12489 doi:10.1111/rssb.12489 | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 19 scored citations.