arXiv 25 Sep 2026 · Mathematics — Statistics Theory
arXiv:2609.31958 · PDF · Extracted main text
Instead of having a single "yes" or "no" result from a test of the global null hypothesis that a function is increasing, we propose a multiple testing procedure of the function's increasingness at several points. If the global null is rejected, then multiple testing provides more information about why. If the global null is not rejected, then multiple testing can provide stronger evidence in favor of increasingness, by rejecting null hypotheses that the function is decreasing. Our approach uses high-level assumptions that apply to a broad class of causal and descriptive statistical models. By inverting the proposed multiple testing procedure that controls the familywise error rate, we also generate "inner" and "outer" confidence sets for the set of points at which the function is increasing. With high asymptotic probability, the inner confidence set is contained within the true set, whereas the outer confidence set contains the true set. We also improve power with stepdown and two-stage procedures. Simulation and empirical examples illustrate the new methodology, and all code is provided.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | barticle Romano, J.P., Wolf, M.: Testing for monotonicity in expecte… (2013) ) 10.1016/j.jempfin.2013.05.001 barticle | 1.000 | 7 | 3 | 100% |
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| 3 | barticle Manski, C.F., Pepper, J.V.: Monotone instrumental variables… (2000) ) 10.1111/1468-0262.t01-1-00144a barticle | 0.874 | 5 | 2 | 100% |
| 4 | barticle Romano, J.P., Shaikh, A.M., Wolf, M.: A practical two-step… (1979) –2002 (2014) 10.3982/ECTA11011 barticle | 0.874 | 5 | 2 | 100% |
| 5 | barticle Kaplan, D.M.: Inference on consensus ranking of distributio… (2024) ) 10.1080/07350015.2023.2252040 barticle | 0.811 | 4 | 2 | 100% |
| 6 | barticle Holm, S.: A simple sequentially rejective multiple test pro… (1979) ) barticle | 0.644 | 2 | 2 | 100% |
| 7 | bbook Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S… (2002) ) | 0.644 | 2 | 2 | 100% |
| 8 | bbook R Core Team: R: A Language and Environment for Statistical Com… (2024) ) | 0.644 | 2 | 2 | 100% |
| 9 | barticle Andrews, D.W.K.: Heteroskedasticity and autocorrelation con… (1991) ) 10.2307/2938229 barticle | 0.511 | 2 | 1 | 100% |
| 10 | barticle Armstrong, T.B., Shen, S.: Inference on optimal treatment a… (2023) ) 10.1007/s42973-023-00138-1 barticle | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 45 scored citations.