Scandinavian Journal of Statistics · 2012 · 90 citations · 21 references
New MeasureBusinessEconometricsRegression Dependence OrderBiostatisticsStatistical InferenceRegression AnalysisRegression DependencePublic HealthDependence ModelingMultivariate AnalysisStatisticsFunctional Data AnalysisCopulas
The article introduces a framework and the concept of regression dependence order to compare bivariate distributions based on their regression dependence. The authors define a new non‑parametric measure of regression dependence, construct a consistent estimator, analyze its asymptotic properties, and assess finite‑sample performance via simulation. The measure is monotone in the regression dependence order, reaches its extremes at independence and almost sure functional dependence, and its estimator demonstrates consistent asymptotic behavior and favorable finite‑sample properties. Abstract.
Abstract. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.
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