"Multivariate Dispersion, Central Regions, and Depth": The Lift Zonoid Approach

177 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On the Concept of Depth for Functional Data (2009, background): “In Mosler (2002) a depth-based rank test for detecting difference in scale and location is described.”
Depth Statistics (2012, background): “|X) are discussed in Mosler (2002).”
Multidimensional generalized Gini indices (2005, background): “For a discussion of distance-and volume-based multidimensional Ginis, with further references to the literature, see Mosler (2002).”
Monge-Kantorovich Depth, Quantiles, Ranks and Signs (2014, background): “The appealing properties of halfspace depth are well known and well documented: see Donoho and Gasko [15], Mosler [43], Koshevoy [36], Ghosh and Chaudhuri [20], Cuestas-Albertos and Nieto-Reyes [9], Hassairi and Regaieg [30], to cite only a few.”
Integrated depth for functional data: statistical properties and consistency (2016, background): “In general, (D3) is not satisfied for sD as noted by Mosler ([29], p. 120) and the sufficient conditions on Q for the quasi-concavity to hold for are, to the best of our knowledge, unknown.”
Choosing Among Notions of Multivariate Depth Statistics (2020, background): “Mahalanobis depth, being a continuous function of moments, obviously satisfies a Law of Large Numbers; the same holds for halfspace depth (Donoho and Gasko, 1992), simplicial depth (Dümbgen, 1992), and zonoid depth (Mosler, 2002, Th. 4.6).”