RT Generic
T1 Depth functions based on a number of observations of a random vector
A1 Cascos Fernández, Ignacio
A2 Universidad Carlos III de Madrid. Departamento de Estadística, 
AB We present two statistical depth functions given in terms of the random variable defined as theminimum number of observations of a random vector that are needed to include a fixed givenpoint in their convex hull. This random variable measures the degree of outlyingness of a pointwith respect to a probability distribution. We take advantage of this in order to define the newdepth functions. Further, a technique to compute the probability that a point is included in theconvex 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 andwe derive a depth function from it. The relation of this depth function with the linear convexstochastic order is investigated and a multivariate extension of the Gini mean difference isdefined in terms of the selection expectation of the convex hull of two independent copies of arandom vector.
YR 2007
FD 2007-04
LK https://hdl.handle.net/10016/700
UL https://hdl.handle.net/10016/700
LA eng
LA eng
DS e-Archivo
RD 2 may. 2024