Computing zonoid trimmed regions of bivariate data sets

In data analyis an important task is to identify sets of points that are central in a data set {x₁, …, x_n} ⊂ ℝd A set of points that is central in some sense is called a trimmed region. In the univariate case a trimmed region is, e.g., the closed interval between two proper quantiles. Nolan (1992) and Massé and Theodorescu (1994) introduced concepts of trimmed regions, based on a multivariate analogue of the quantile function, suggested by Tukey (1975) and Eddy (1983). These concepts can be seen as generalizations of the univariate interquantile intervals.