[Forum SIS] Seminar: Omar El-Dakkak on Thursday 11JUNE2009 at 4:30pm (DEC Bocconi)

[Marco Bonetti]

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                                                      ANNOUNCEMENT
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On THURSDAY, June 11th 2009 at 4:30pm in Room C
(Via Sarfatti 25, Milan) of Bocconi University

                                             Omar El-Dakkak
            Laboratoire de Statistique Théorique et Appliquée
                    Université Pierre et Marie Curie (Paris VI)

will hold the seminar:

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"Hoeffding decompositions and urn sequences"

Abstract:

Let X[1,∞) = {Xn : n ≥ 1} be a sequence of random variables. We say  
that
the sequence is Hoeffding-decomposable if, for all n ≥ 2; any  
symmetric statistic
T (X1, ..., Xn) admits a unique representation as a sum of (n + 1)  
uncorrelated
U-Statistics with completely degenerated kernels of increasing orders.
Introduced for the first time in a seminal paper by W. Hoeffding in  
1948,
the so called Hoeffding decompositions grew to become one of the  
fundamental
techniques for proving asymptotic distributional results. This has
definitely been the case for i.i.d. sequences; as for dependent  
sequences, only
extractions without replacement from finite populations (see Bloznelis  
and
Götze [2001, 2002]) had been investigated before the theory was  
generalized
to general exchangeable sequences in Peccati [2004]. In fact, in that  
reference
a characterization of Hoeffding-decomposable sequences in terms of a
technical condition the author named weak independence is obtained. In
El-Dakkak and Peccati [2008], we seek a more transparent  
characterization
of Hoeffding decomposable exchangeable sequences and focus on sequences
taking values in a finite set D. In the case in which D = {0, 1}, we  
show that
the only Hoeffding decomposable exchangeable sequences are i.i.d.  
sequences
and two-colour Pólya sequences. When D is an arbitrary finitie set, we  
ob-
tain a partial generalization of the two-colour case. The full  
generalization is
obtained in El-Dakkak, Peccati and Prünster [2009]: more precisely, we  
show
that multicolour Pólya sequences are the only D-valued purely  
exchangeable
sequences that are Hoeffding decomposable.
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You are warmly invited to participate.

Sincerely,

Marco Bonetti


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Marco Bonetti
Department of Decision Sciences
Bocconi University
Via Guglielmo Roentgen 1
20136 Milan, Italy
Tel +39 02 58365670
Fax +39 02 58365634

>

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