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Enhanced power enhancements for testing many moment equalities: Beyond the $2$- and $\infty$-norm

Anders Bredahl Kock, David Preinerstorfer

arXiv 25 Jul 2024 · Econometrics · publishedJournal of the American Statistical Association (2025)

arXiv:2407.17888 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Contemporary testing problems in statistics are increasingly complex, i.e., high-dimensional. Tests based on the $2$- and $\infty$-norm have received considerable attention in such settings, as they are powerful against dense and sparse alternatives, respectively. The power enhancement principle of Fan et al. (2015) combines these two norms to construct improved tests that are powerful against both types of alternatives. In the context of testing whether a candidate parameter satisfies a large number of moment equalities, we construct a test that harnesses the strength of all $p$-norms with $p\in[2, \infty]$. As a result, this test is consistent against strictly more alternatives than any test based on a single $p$-norm. In particular, our test is consistent against more alternatives than tests based on the $2$- and $\infty$-norm, which is what most implementations of the power enhancement principle target. We illustrate the scope of our general results by using them to construct a test that simultaneously dominates the Anderson-Rubin test (based on $p=2$), tests based on the $\infty$-norm and power enhancement based combinations of these in terms of consistency in the linear instrumental variable model with many instruments.

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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
1Kock, A. B. and D. Preinerstorfer (2023) Consistency of p-norm based tests in high dimensions: Characterization, monotonicity, domination self1.000238100%
2Mikusheva, A. and L. Sun (2022) Inference with many weak instruments1.00064100%
3Fan, J., Y. Liao, and J. Yao (2015) Power enhancement in high-dimensional cross-sectional tests1.00054100%
4Fang, X. and Y. Koike (2024) Large-dimensional central limit theorem with fourth-moment error bounds on convex sets and balls0.92843100%
5Abdalla, P. and N. Zhivotovskiy (2024) Covariance estimation: Optimal dimension-free guarantees for adversarial corruption and heavy tails0.87462100%
6Oliveira, R. I. and Z. F. Rico (2022) Improved covariance estimation: optimal robustness and sub-Gaussian guarantees under heavy tails0.81142100%
7Bentkus, V (2003) On the dependence of the Berry–Esseen bound on dimension0.73732100%
8Mendelson, S. and N. Zhivotovskiy (2020) Robust covariance estimation under $L_4-L_2$ norm equivalence0.73732100%
9Belloni, A., D. Chen, V. Chernozhukov, and C. Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain0.64422100%
10Boot, T. and J. W. Ligtenberg (2023) Identification- and many instrument-robust inference via invariant moment conditions0.64422100%

Showing the top 10 of 67 scored citations.