On Quantifying Dependence: A Framework for Developing Interpretable Measures

摘要: We present a framework for selecting and developing measures of dependence when the goal is quantification relationship between two variables, not simply establishment its existence. Much literature on focused, at least implicitly, detection or revolves around inclusion/exclusion particular axioms discussing which satisfy said axioms. In contrast, we start with only few nonrestrictive guidelines focused existence, range interpretability, provide very open flexible framework. For quantification, most crucial notion whose foundation can be found in work Goodman Kruskal [Measures Association Cross Classifications (1979) Springer], importance seen popularity tools such as $R^2$ linear regression. While probabilistic interpretations their measures, demonstrate how more general information used to achieve same goal. To that end, strategy building designed allow practitioners tailor needs. many well-known fit our conclude paper by presenting real data examples. Our first example explores U.S. income education where this methodology help guide selection development measure. second examines functional data, illustrates them using geomagnetic storms.