Multiple testing of a function’s monotonicity

Wei Zhao and David M. Kaplan ()
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Wei Zhao: University of Missouri, Department of Economics
David M. Kaplan: University of Missouri, Department of Economics

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 34, issue 4, No 8, 1080-1103

Abstract: Abstract 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.

Keywords: Familywise error rate; Inner confidence set; Multiple testing procedure; Outer confidence set; 62J15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11749-025-00986-6

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