Group for Research in Decision Analysis

# Weighted methods for multivariate rank statistics

## Jean-François Plante – Associate Professor, Department of Decision Sciences, HEC Montréal, Canada

This talk is about weighted methods for copulas and coefficients of correlation based on ranks. Suppose first that m samples of $$p$$- dimensional data are available, that all samples share the same dependence structure (copula), but that their marginal distributions are different. We calculate the ranks within each sample, then, using appropriate weights, we obtain weighted empirical copulas, weighted coefficients of correlation, and the weighted pseudo-likelihood.

Properties of these estimates are presented and we show how they can be used to build nonparametric correlograms. Finally, we also consider a different paradigm where samples may feature different copulas, and one population is identified as the target for inference. We then illustrate that it is possible to build data-based weights that combine information from all the m populations without making assumptions on their similarities.