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Fast Test Inversion for Resampling Methods

Ian Xu

arXiv 16 Dec 2025 · Econometrics

arXiv:2512.14024 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Randomization-based inference commonly relies on grid search methods to construct confidence intervals by inverting hypothesis tests over a range of parameter values. While straightforward, this approach is computationally intensive and can yield conservative intervals due to discretization. We propose a novel method that exploits the algebraic structure of a broad class of test statistics--including those with variance estimators dependent on the null hypothesis--to produce exact confidence intervals efficiently. By expressing randomization statistics as rational functions of the parameter of interest, we analytically identify critical values where the test statistic's rank changes relative to the randomization distribution. This characterization allows us to derive the exact p-value curve and construct precise confidence intervals without exhaustive computation. For cases where the parameter of interest is a vector and a confidence region is needed, our method extends by calculating and storing the coefficients of the polynomial functions involved. This approach enables us to compute approximate p-value functions and confidence regions more efficiently than traditional grid search methods, as we avoid recalculating test statistics from scratch for each parameter value. We illustrate our method using tests from Pouliot (2024) and extend it to other randomization tests, such as those developed by DiCiccio and Romano (2017) and D'Haultfœuille and Tuvaandorj (2024). Our approach significantly reduces computational burden and overcomes the limitations of traditional grid search methods, providing a practical and efficient solution for confidence interval and region construction in randomization-based inference.

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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Pouliot, Guillaume A (2024) An Exact $t$-Test1.000147100%
2D'Haultfœuille, Xavier and Tuvaandorj, Purevdorj (2024) A Robust Permutation Test for Subvector Inference in Linear Regressions1.00094100%
3DiCiccio, Cyrus J and Romano, Joseph P (2017) Robust permutation tests for correlation and regression coefficients1.00073100%
4Wooldridge, Jeffrey M (2020) Introductory Econometrics: A Modern Approach (7e)0.51121100%
5Paul H. Garthwaite (1996) Confidence Intervals from Randomization Tests0.51121100%
6Cai, Yong and Canay, Ivan A. and Kim, Deborah and Shaikh, Azeem M (2023) Inference for Linear Regression Models with Many Covariates0.40511100%
7Leying Guan (2024) A Conformal Test of Linear Models via Permutation-Augmented Regressions0.40511100%
8Bruce E. Hansen (2022) Probability and Statistics for Economists0.40511100%
9Tadeusz Kaczorek (2007) Polynomial and Rational Matrices: Applications in Dynamical Systems Theory0.40511100%

Showing the top 9 of 9 scored citations.