Computation of quantile sets for bivariate ordered data

Abstract

Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data points in form of a vector order in two dimensions. The bivariate case deserves special attention since two-dimensional vector orders are much simpler to handle than such orders in higher dimensions. Several examples illustrate how the algorithms work and what kind of conclusions can be drawn with the proposed approach. As a new feature, it is observed that the computational effort depends on how much the original data points are aligned with respect to the vector order.