Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Computing depth contours of bivariate point clouds
Computational Statistics & Data Analysis - Special issue on classification
Computing location depth and regression depth in higher dimensions
Statistics and Computing
Efficient computation of location depth contours by methods of computational geometry
Statistics and Computing
Depth-based inference for functional data
Computational Statistics & Data Analysis
The expected convex hull trimmed regions of a sample
Computational Statistics
Weighted-mean trimming of multivariate data
Journal of Multivariate Analysis
Computing projection depth and its associated estimators
Statistics and Computing
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A probability distribution on Euclidean d-space can be described by its zonoid regions. These regions form a nested family of convex sets around the expectation, each being closed and bounded. The zonoid regions of an empirical distribution introduce an ordering of the data that has many applications in multivariate statistical analysis, e.g. cluster analysis, tests for multivariate location and scale, and risk analysis. An exact algorithm is developed to constructing the zonoid regions of a d-variate empirical distribution by their facets when d=3. The vertices of the region and their adjacency are characterized, and a procedure is suggested by which all vertices and facets can be determined. The algorithm is available as an R-package.