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Numerical Analysis of Test Optimality

Philipp Ketz, Adam McCloskey, Jan Scherer

arXiv 22 Dec 2025 · Econometrics

arXiv:2512.19843 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In nonstandard testing environments, researchers often derive ad hoc tests with correct (asymptotic) size, but their optimality properties are typically unknown a priori and difficult to assess. This paper develops a numerical framework for determining whether an ad hoc test is effectively optimal - approximately maximizing a weighted average power criterion for some weights over the alternative and attaining a power envelope generated by a single weighted average power-maximizing test. Our approach uses nested optimization algorithms to approximate the weight function that makes an ad hoc test's weighted average power as close as possible to that of a true weighted average power-maximizing test, and we show the surprising result that the rejection probabilities corresponding to the latter form an approximate power envelope for the former. We provide convergence guarantees, discuss practical implementation and apply the method to the weak instrument-robust conditional likelihood ratio test and a recently-proposed test for when a nuisance parameter may be on or near its boundary.

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36
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133
in-text mentions
36
distinct cited
4
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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
1D. W. K. Andrews and M. J. Moreira and J. H. Stock (2006) Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression1.00083100%
2D. W. K. Andrews and M. J. Moreira and J. H. Stock (2008) Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments1.00073100%
3A. Aradillas Fernández and J. Blanchet and J. L. Montiel Olea and C.… (2025) Approximate Least-Favorable Distributions and Nearly Optimal Tests via Stochastic Mirror Descent1.00064100%
4H. Moreira and M. J. Moreira (2013) Contributions to the Theory of Optimal Tests1.00064100%
5Andrews, Donald W. K. and Marmer, Vadim and Yu, Zhengfei (2019) On optimal inference in the linear IV model1.00053100%
6G. Elliott and U. K. Müller and M. W. Watson (2015) Nearly Optimal Tests when a Nuisance Parameter is Present Under the Null Hypothesis0.98727696%
7G. F. Cox (2024) A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality0.97413392%
8N. Van de Sijpe and F. Windmeijer (2023) On the Power of the Conditional Likelihood Ratio and Related Tests for Weak-Instrument Robust Inference0.87492100%
9Guggenberger, Patrik and Kleibergen, Frank and Mavroeidis, Sophocles (2019) A more powerful subvector Anderson Rubin test in linear instrumental variables regression0.81142100%
10P. Ketz and A. McCloskey (2025) Short and Simple Confidence Intervals when the Directions of Some Effects are Known self0.81142100%

Showing the top 10 of 36 scored citations.