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New Axioms for Dependence Measure and Powerful Tests

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  • Hrishikesh Vinod

    (Fordham University)

Abstract

Statistical measure(s) of dependence (MOD) between variables are essential for most empirical work. We show that Renyi’s postulates from the 1950s are responsible for serious MOD limitations. (i) They rule out examples when one of the variables is deterministic (like time or age), (ii) They are always positive, implying no one-tailed significance tests. (iii) They disallow ubiquitous asymmetric MOD. Many MOD exist in the literature, including those from 2022 and 2025, share these limitations because they fail to satisfy our three new axioms. We also describe a new implementation of a powerful one-sided test for the null of zero Pearson correlation with Taraldsen’s exact sampling distribution and provide a new table for practitioners. We include a published example where Taraldsen’s test makes a practical difference. The code to implement all our proposals is in R packages.

Suggested Citation

  • Hrishikesh Vinod, 2025. "New Axioms for Dependence Measure and Powerful Tests," Fordham Economics Discussion Paper Series dp2025-02er:dp2025-02, Fordham University, Department of Economics.
    • Handle: RePEc:frd:wpaper:dp2025-02er:dp2025-02
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