Seminario de Probabilidad y Estadística
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
Viernes 31/3 a las 10:30
Facultad de Ciencias Económicas y Administración (entrada por Lauro Muller).
Contacto: Alejandro Cholaquidis - acholaquidis@hotmail.com
Link:
https://salavirtual-udelar.zoom.us/j/88544669179?pwd=UlBHdWRWdEZVMGw0ak…
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