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A novel positive dependence property is introduced, called positive measureinducing (PMI for short), being fulfilled by numerous copula classes, includingGaussian, Fr\'echet, Farlie-Gumbel-Morgenstern and Frank copulas; it isconjectured that even all positive quadrant dependent Archimedean copulas meetthis property. From a geometric viewpoint, a PMI copula concentrates more massnear the main diagonal than in the opposite diagonal. A striking feature of PMIcopulas is that they impose an ordering on a certain class of copula-inducedmeasures of concordance, the latter originating in Edwards et al. (2004) andincluding Spearman's rho $\rho$ and Gini's gamma $\gamma$, leading to numerousnew inequalities such as $3 \gamma \geq 2 \rho$. The measures of concordancewithin this class are estimated using (classical) empirical copulas and theintrinsic 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 fordetecting whether the underlying dependence structure of a given sample is PMI,which in turn can be used for excluding certain copula families from modelbuilding. The excellent performance of the tests is demonstrated in asimulation study and by means of a real-data example.

A novel positive dependence property and its impact on a popular class of concordance measures