Comparing Bivariate Random Vectors by Means of Statistical Preference

StochasticRos, J.Pérez-Fernández, R.Montes, I. orders are probabilistic tools used for comparing random quantities. Statistical preference is a stochastic ordering with two main features: firstly, the comparison is based on the joint distribution of the random variables, thus considering potential dependence between them. Secondly, it is accompanied by a winning probability, which measures the strength of the preference. This contribution proposes several ways to extend statistical preference for comparing (bivariate) random vectors. These proposals follow three different approaches: (i) aggregating the winning probabilities of each component, (ii) computing the winning probabilities between the aggregated random vectors, or (iii) defining a purely bivariate winning probability. Besides investigating these properties, the relationships between them and the componentwise median are studied.