Depth functions based on a number of observations of a random vector

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dc.contributor.author Cascos Fernández, Ignacio
dc.contributor.editor Universidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned 2007-04-19T09:42:51Z
dc.date.available 2007-04-19T09:42:51Z
dc.date.issued 2007-04
dc.identifier.uri http://hdl.handle.net/10016/700
dc.description.abstract We present two statistical depth functions given in terms of the random variable defined as the minimum number of observations of a random vector that are needed to include a fixed given point in their convex hull. This random variable measures the degree of outlyingness of a point with respect to a probability distribution. We take advantage of this in order to define the new depth functions. Further, a technique to compute the probability that a point is included in the convex hull of a given number of i.i.d. random vectors is presented. Consider the sequence of random sets whose n-th element is the convex hull of $n$ independent copies of a random vector. Their sequence of selection expectations is nested and we derive a depth function from it. The relation of this depth function with the linear convex stochastic order is investigated and a multivariate extension of the Gini mean difference is defined in terms of the selection expectation of the convex hull of two independent copies of a random vector.
dc.format.extent 392297 bytes
dc.format.mimetype application/pdf
dc.language.iso eng
dc.language.iso eng
dc.relation.ispartofseries UC3M Working papers. Statistics and Econometrics
dc.relation.ispartofseries 07-07
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Convex hull
dc.subject.other Depth function
dc.subject.other Linear convex stochastic order
dc.subject.other Multivariate Gini mean difference
dc.subject.other Random set
dc.subject.other Selection expectation
dc.subject.other Simplicial depth
dc.subject.other Sphere coverage
dc.title Depth functions based on a number of observations of a random vector
dc.type workingPaper
dc.subject.eciencia Estadística
dc.rights.accessRights openAccess
dc.identifier.repec ws072907
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