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Measures of independence and functional dependence
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We follow up on Shi et al's (2020) and Cao's and my (2020) work on the local power of a new test for independence, Chatterjee (2019), and its relation to the local power properties of classical tests. We show quite generally that for testing independence with local alternatives either Chatterjee's rank test has no power, or it may be misleading: The Blum, Kiefer, Rosenblatt, and other omnibus classical rank tests do have some local power in any direction other than those where significant results may be misleading. We also suggest methods of selective inference in independence testing. Chatterjee's statistics like Renyi's (1959) also identified functional dependence. We exhibit statistics which have better power properties than Chatterjee's but also identify functional dependence.
Forward citations
Cited by 3 Pith papers
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A symmetrized Chatterjee rank correlation matrix has a semicircle spectral limit, plus a central limit theorem and independence tests that detect zero-linear-correlation dependence.
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A rank-based nearest-neighbor graph yields a scale-invariant Azadkia-Chatterjee correlation coefficient that is consistent and, for d ≠ 2, asymptotically normal under independence.
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A Modified Dependence Measure Related to Chatterjee's Rank Correlation: Theoretical Properties and Asymptotic Analysis
The proposed right-continuous variant of the DSS measure is not new for continuous variables, and the theorem giving its null distribution is contradicted by a simple calculation.
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