Permutation testing in high-dimensional linear models: an empirical investigation

Hemerik, Jesse; Thoresen, Magne; Finos, Livio

doi:10.1080/00949655.2020.1836183

Cited by 11 publications

(8 citation statements)

References 34 publications

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“…This test is based on a bias-corrected estimation and an asymptotic upper bound of its distribution. (iii) "FL" is the Freedman-Lane HD test proposed by Hemerik et al (2020) with the test statistic based on the generalized partial correlation. (iv) "DR" is the Double Residualization method in Hemerik et al (2020), which residualizes both Y and X and tests the sample correlation.…”

Section: Results Of Varying Parametersmentioning

confidence: 99%

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Correcting Confounding via Random Selection of Background Variables

Chen¹,

Minorics²,

Janzing³

2022

Preprint

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We propose a method to distinguish causal influence from hidden confounding in the following scenario: given a target variable Y , potential causal drivers X, and a large number of background features, we propose a novel criterion for identifying causal relationship based on the stability of regression coefficients of X on Y with respect to selecting different background features. To this end, we propose a statistic V measuring the coefficient's variability. We prove, subject to a symmetry assumption for the background influence, that V converges to zero if and only if X contains no causal drivers. In experiments with simulated data, the method outperforms state of the art algorithms. Further, we report encouraging results for real-world data. Our approach aligns with the general belief that causal insights admit better generalization of statistical associations across environments, and justifies similar existing heuristic approaches from the literature.

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Section: Results Of Varying Parametersmentioning

confidence: 99%

“…Every high-dimensional regression method can be combined with this permutation method. For instance, Hemerik et al (2020) proposed the ridge regression to estimate γ:…”

Section: A1 Freedman-lane Permutation Methodsmentioning

confidence: 99%

Correcting Confounding via Random Selection of Background Variables

Chen¹,

Minorics²,

Janzing³

2022

Preprint

View full text Add to dashboard Cite

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“…The works by Anderson and Legendre (1999); Winkler et al (2014) review and compare a number of previously proposed permutation methods for inference in linear models with nuisance parameters. Hemerik et al (2020b) show empirically that permutation tests can control type I error even in certain high dimensional linear models. Hemerik et al (2020a) develop tests for potentially mis-specified generalized linear models by randomly flipping signs of score contributions.…”

Section: Related Workmentioning

confidence: 97%

Consistency of invariance-based randomization tests

Dobriban¹

2021

Preprint

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Invariance-based randomization tests-such as permutation tests-are an important and widely used class of statistical methods. They allow drawing inferences with few assumptions on the data distribution. Most work focuses on their type I error control properties, while their consistency properties are much less understood.We develop a general framework and a set of results on the consistency of invariancebased randomization tests in signal-plus-noise models. Our framework is grounded in the deep mathematical area of representation theory. We allow the transforms to be general compact topological groups, such as rotation groups. Moreover, we allow actions by general linear group representations.We apply our framework to a number of fundamental and highly important problems in statistics, including sparse vector detection, testing for low-rank matrices in noise, sparse detection in linear regression, symmetric submatrix detection, and two-sample testing. Perhaps surprisingly, we find that randomization tests can adapt to problem structure and detect signals at the same rate as tests with full knowledge of the noise distribution. Contents

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“…For each ANOVA, the group-effect significance was estimated conducting a permutation test (2000 randomisations) on the F-statistics (105) This procedure was chosen as permutation tests are robust to violations of parametric statistics assumptions such as non-normality and heteroscedasticity (106), and thus well-suited for statistical analyses on datasets with relatively small and unbalanced sample sizes. All variables showing a significant group-effect (here and in the following, p-values lower than 0.05 will be considered significant), were then submitted to a post-hoc analysis with the aim of assessing which couples of groups showed significant differences.…”

Section: Statistical Proceduresmentioning

confidence: 99%

Catastrophisation, chronic pain and sexuality: a cross-sectional investigation in fibromyalgia and rheumatoid arthritis

Piarulli

Conversano

Ciacchini

et al. 2021

Clinical and Experimental Rheumatology

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Objective. In the present study we investigate the putative differences in pain catastrophising (PC), pain perception (PP), sexual functioning (SF), satisfaction (SS), and overall quality of life between fibromyalgia (FM) and rheumatoid arthritis (RA) patients as compared to healthy controls (HC). Methods. Fifty-seven native Italianspeaking female individuals suffering either from FM or RA and thirty-eight healthy female controls (FM=40; RA=17; HC=38) were submitted to a semi-structured interview aimed at assessing PP intensity (Visual Analogue Scale; VAS), general health conditions (36-

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Permutation testing in high-dimensional linear models: an empirical investigation

Cited by 11 publications

References 34 publications

Correcting Confounding via Random Selection of Background Variables

Correcting Confounding via Random Selection of Background Variables

Consistency of invariance-based randomization tests

Catastrophisation, chronic pain and sexuality: a cross-sectional investigation in fibromyalgia and rheumatoid arthritis

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