 A simple measure of conditional dependenceMona Azadkia and Sourav Chatterjee LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library Abstract: We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1, . . . , Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0, 1], where the limit is 0 if and only if Y and Z are conditionally independent given X1, . . . , Xp, and is 1 if and only if Y is equal to a measurable function of Z given X1, . . . , Xp. Moreover, it has a natural interpretation as a nonlinear generalization of the familiar partial R2 statistic for measuring conditional dependence by regression. Using this statistic, we devise a new variable selection algorithm, called Feature Ordering by Conditional Independence (FOCI), which is model-free, has no tuning parameters, and is provably consistent under sparsity assumptions. A number of applications to synthetic and real datasets are worked out. Keywords: conditional dependence; non-parametric measures of association; variable selection (search for similar items in EconPapers) Published in Annals of Statistics, 31, December, 2021. ISSN: 0090-5364 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:125584 Access Statistics for this paper More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC. |
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