A novel positive dependence property and its impact on a popular class of concordance measures
提出一种新的正相依性质PMI，许多copula满足该性质，它给出一类和谐度量之间的不等式，并基于经验copula构建了检验PMI的渐近检验，通过模拟和实例验证了其良好性能。
A novel positive dependence property is introduced, called positive measure inducing (PMI for short), being fulfilled by numerous copula classes, including Gaussian, Student t, Fréchet, Farlie–Gumbel–Morgenstern and Frank copulas; it is conjectured that even all positive quadrant dependent Archimedean copulas meet this property. From a geometric viewpoint, a PMI copula concentrates more mass near the main diagonal than in the opposite diagonal. A striking feature of PMI copulas is that they impose an ordering on a certain class of copula-induced measures of concordance, the latter originating in Edwards et al. (2004) and including Spearman’s rho ρ and Gini’s gamma γ, leading to numerous new inequalities such as 3γ≥2ρ. The measures of concordance within this class are estimated using (classical) empirical copulas and the intrinsic construction via empirical checkerboard copulas, and the estimators’ asymptotic behaviour is determined. Building upon the presented inequalities, asymptotic tests are constructed having the potential of being used for detecting whether the underlying dependence structure of a given sample is PMI, which in turn can be used for excluding certain copula families from model building. The excellent performance of the tests is demonstrated in a simulation study and by means of a real-data example.