Multivariate measures of concordance

Multivariate measures of concordance

In 1984 Scarsini introduced a set of axioms for measures of concordance of ordered pairs of continuous random variables. We exhibit an extension of these axioms to ordered n-tuples of continuous random variables, n ≥ 2. We derive simple properties of such measures, give examples, and discuss the relation of the extended axioms to multivariate measures of concordance previously discussed in the ...

Some properties of multivariate measures of concordance

We explore the consequences of a set of axioms which extend Scarsini’s axioms for bivariate measures of concordance to the multivariate case and exhibit the following results: (1) A method of extending measures of concordance from the bivariate case to arbitrarily high dimensions. (2) A formula expressing the measure of concordance of the random vectors (±X1, · · · ,±Xn) in terms of the measure...

Relationship between multivariate concordance and risk measures

The question about the definition of concordance between random vectors is an open problem because there is not an unanimous opinion about its meaning and its appropriate definition. Also the definition of multivariate risk measures encounters many difficulties. In this paper we want to investigate the relationship between these multivariate measures, essentially based on the relation between r...

Multivariate copulas: Transformations, symmetry, order and measures of concordance

A repeated measures concordance correlation coefficient.

The concordance correlation coefficient is commonly used to assess agreement between two raters or two methods of measuring a response when the data are measured on a continuous scale. However, the situation may arise in which repeated measurements are taken for each rater or method, e.g. longitudinal studies in clinical trials or bioassay data with subsamples. This paper proposes a coefficient...