[Forum SIS] Avviso di seminario

[Anna Paganoni]

In data 31-5-2011, presso l'Aula Seminari F. Saleri,

VI Piano MOX- Dipartimento di Matematica, Politecnico di Milano,
nell'ambito delle iniziative MOX, si svolgera' un pomeriggio di studio
sul tema

"Nonparametric combination methods for multivariate hypothesis testing"

Tutti gli interessati sono invitati a partecipare.

Programma:

Ore 14:30 - 15:30:

Relatore: Prof. Fortunato Pesarin, Department of Statistical Sciences,
University of Padua - Italy

Titolo: Parametric Versus Nonparametrics: Two Alternative Approaches?
(with emphasis on permutation methods).

Abstract: In recent years permutation testing methods have increased both
in number of applications and in solving complex multivariate problems.
When available permutation tests are essentially of an exact nonparametric
nature in a conditional context, where conditioning is on the pooled
observed data set which is often a set of sufficient statistics in the
null hypothesis. Whereas, the reference null distribution of most
parametric tests is only known asymptotically. Thus, for most sample sizes
of practical interest, the possible lack of efficiency of permutation
solutions may be compensated by the lack of approximation of parametric
counterparts. There are many complex multivariate problems, quite common
in empirical sciences, which are difficult to solve outside the
conditional framework and in particular outside the method of
nonparametric combination (NPC) of dependent permutation tests especially
when the number of observed variables is larger than sample size. In this
seminar we discuss this method along with a number of applications in
experimental and observational situations (e.g. multi-aspect testing,
multivariate stochastic ordering, robust testing, multi-sided
alternatives, testing for survival functions).


Ore 15:30-16:00: coffee break


Ore 16:00 - 17:00:

Relatore: Dr. Chiara Brombin ,CUSSB (University Centre of Statistics in
the Biomedical Sciences)
Vita-Salute San Raffaele University

Titolo: How to study complex shapes when the sample size cannot be increased

Abstract: Statistical shape analysis is a cross-disciplinary field,
allowing for ap-
plications in biology, geology, medicine and many other sciences, since
it is
characterized by flexible theory and techniques, potentially adaptable
to any appropriate
configuration matrices.
The statistical community has shown an increased interest in shape
analysis in the
last decade and lots of efforts have been addressed to the development
of powerful
statistical methods for the comparison of shapes. Actually, traditional
inferential
methods make use of congurations of landmarks optimally superimposed using a
least-squares procedure or analyze matrices of interlandmark distances.
For a de-
tailed review, see Rohlf (2000). For example, in the two independent
sample case,
a practical method for comparing the mean shapes in the two groups is to
use the
Procrustes tangent space coordinates, if data are concentrated,
calculate the Ma-
halanobis distance and then the Hotelling's T2 test statistic. Under the
assumption
of isotropy, another simple approach is to work with statistics based on
the squared
Procrustes distance and then consider the Goodall's F test statistic.
Despite their
widespread use, on the one hand it is well known that Hotelling's T2
test may not
be very powerful unless there are a large number of observations
available, and on
the other hand the underlying model required by Goodall's F test is very
restric-
tive.
Hence, these methods are based on strong assumptions and often require
large sam-
ple size while, in practice, researchers have to deal with few
individuals and many
landmarks, implying over-dimensioned spaces and loss of power.
In light of all these considerations, we propose an extension of the
nonparametric
combination (NPC) methodology to shape analysis. We illustrate how it is
possible
to obtain powerful tests in a nonparametric framework by increasing the num-
ber of informative variables while leaving the number of cases fixed. In
particular,
the power of the suggested tests increases when the number of processed
variables
increases, provided that the induced noncentrality parameter increases,
and this re-
sult holds even when the number of variables is larger than the
permutation sample
space (Brombin, Pesarin and Salmaso, 2010). Applications to real case
studies in
biology and in rhinoseptoplasty surgery are shown.



-- 

Anna Maria Paganoni
MOX - Modeling and Scientific Computing
Dipartimento di Matematica "F. Brioschi"
Politecnico di Milano
Piazza Leonardo da Vinci, 32
I-20133 Milano - Italy
tel. +39 02 2399 4574
fax. +39 02 2399 4568
e.mail: anna.paganoni a polimi.it