[Probabilidad-Estadistica-Seminario] Seminario de Probabilidad y Estadística - Ricardo Fraiman (Udelar)

[seminarios en cmat.edu.uy]

Seminario de Probabilidad y Estadística
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Título: "A Cramér--Wold theorem for elliptical distributions"

Expositor: Ricardo Fraiman (Udelar)

Resumen:
 
According to a well-known theorem of Cramér and Wold,   if P and Q are two Borel
probability measures on R^d   whose projections P_L,Q_L onto each line L in R^d
satisfy P_L=Q_L, then P=Q.   Our main result is that, if P and Q are both
elliptical distributions,   then, to show that P=Q, it suffices merely to check
that P_L=Q_L for a certain set of (d^2+d)/2 lines L.   Moreover (d^2+d)/2 is
optimal. The class of elliptical distributions contains the Gaussian
distributions as well as many other multivariate distributions of interest.
Our theorem contrasts with  other variants of the Cram\'er--Wold theorem,   in
that no assumption is made about the finiteness of moments of P and Q.   We use
our results to derive a statistical test for equality of elliptical
distributions,   and carry out a small simulation study of the test, comparing
it   with other tests from the literature. We also give an   application to
learning (binary classification), again illustrated with a small simulation.

Joint work with Leonardo Moreno and Thomas Ransford
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Viernes 31/3 a las 10:30, Facultad de Ciencias Económicas y Administración (entrada por Lauro Muller).

Contacto: Alejandro Cholaquidis - acholaquidis en hotmail.com
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Link:

https://salavirtual-
udelar.zoom.us/j/88544669179?pwd=UlBHdWRWdEZVMGw0akpPeEd0VWJzZz09

Página del    seminario : https://pye.cmat.edu.uy/ seminario

Página del grupo: https://pye.cmat.edu.uy/home

Canal de youtube: https://www.youtube.com/channel/UCOPZEOrLSAYPz2qCAL-KqMg/about
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