Robust Permutation Tests For Correlation And Regression Coefficients

By Cyrus DiCiccio, Joseph P. Romano. 2017

107 citations recorded by the source corpus.

ABSTRACT Given a sample from a bivariate distribution, consider the problem of testing independence. A permutation test based on the sample correlation is known to be an exact level α test. However, when used to test the null hypothesis that the samples are uncorrelated, the permutation test can have rejection probability that is far from the nominal level. Further, the permutation test can have a large Type 3 (directional) error rate, whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value, when in fact the true correlation is negative. It will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of Type 1 (or Type 3) errors. These conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution. We will also present asymptotically robust randomization tests for regression coefficients, including a result based on a modified procedure of Freedman and Lane. Simulations and empirical applications are included. Supplementary materials for this article are available online.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/29c8e04ceb99fdd048ffef1bbee62b9856479808

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Citations in the corpus

Covariate-adjusted Fisher randomization tests for the average treatment effect (2020, methodology): “A recent proposal by DiCiccio and Romano (2017) used the τ̂f/s̃ef as the test statistic and constructed the reference distribution by permuting Z.”
Minimax optimality of permutation tests (2020, background): “Finally, we also note that the robustness of permutation tests to violations of the exchangeability condition has been investigated by Romano (1990); Chung and Romano (2013); Pauly et al. (2015); Chung and Romano (2016); DiCiccio and Romano (2017).”
A Statistical Significance Test for Necessary Condition Analysis (2020, methodology): “Since the availability of fast computers, permutation tests have been developed for correlation and regression (Anderson & Robinson, 2001; DiCiccio & Romano, 2017), ANOVA (Anderson, 2001), the general linear model (Winkler, Ridgway, Webster, Smith, & Nichols, 2014), and qualitative comparative…”
Rank‐based procedures in factorial designs: hypotheses about non‐parametric treatment effects (2016, methodology): “A similar behaviour of such Wald-type statistics has been observed for various models; see for example Vallejo et al. (2010), Pauly et al. (2015a) or DiCiccio and Romano (2015).”