Asymmetric Dependence Measurement and Testing
Abstract
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decadeslong literature on statistical dependence reveals that most assume symmetry in the sense that the strength of dependence of Xi on Xj exactly equals the strength of dependence of Xj on Xi. However, we show that such symmetry is often untrue in many realworld examples, being neither necessary nor sufficient. Vinod's (2014) asymmetric matrix R* in [1, 1] of generalized correlation coefficients provides intuitively appealing, readily interpretable, and superior measures of dependence. This paper proposes statistical inference for R* using Taraldsen's (2021) exact sampling distribution of correlation coefficients and the bootstrap. When the direction is known, proposed asymmetric (onetail) tests have greater power.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2211.16645
 arXiv:
 arXiv:2211.16645
 Bibcode:
 2022arXiv221116645V
 Keywords:

 Statistics  Methodology