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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENT SEMINAR}
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\centerline{4:15 p.m., Tuesday, July 16, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Marco Marozzi}
\centerline{\sl Dipartimento di Scienze Statistiche}
\centerline{\sl Alma Mater Studiorum A. D. 1088, Universita` Degli Studi di Bologna}
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\centerline{\bf The Method of the Nonparametric Combination of Dependent
Permutation Tests as a General Tool for Tackling Multivariate and
Multiaspect Testing Problems}
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The method of the Nonparametric Combination (of a finite number) of
Dependent Permutation Tests (NPC) (Pesarin 1988, 2001) as a general tool
for multivariate testing problems (when a set of quite mild conditions
holds), is introduced and discussed.

        In some q-dimensional problems, one single appropriate overall
test statistic $T: R^q \rightarrow R$ is available. Similarly, there are
data transformations $\varphi:R^q \rightarrow R$ of the q-dimensional
data
into univariate derived data $Y=\varphi(X_1,\dots, X_q)$.

        There exist also many multivariate problems for which a single 
overall test is not available (or not easy to find, or too difficult to 
justify). The NPC method may be particularly useful in these cases.
This method is very flexible as well. For example, recently Marozzi
proposed a new way to solve the $K \geq 2$ location problem by using
this general theory in a multiaspect manner. This new solution appears
to be better than the traditional ones for some nonstandard
distributions like the Cauchy, the half-Cauchy and other heavy tailed
distributions. 

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