[Forum SIS] Politecnico di Milano, seminario J.O. Ramsay

[Laura M. Sangalli]

Si avvisa che in data 23-09-2011, alle ore 11:30 precise,
presso Aula Seminari F. Saleri VI Piano MOX - Dipartimento di 
Matematica, Politecnico di Milano,
nell'ambito delle iniziative MOX e del progetto FIRB Futuro in Ricerca 
SNAPFUN, si svolgerà il seguente seminario:

Relatore:
James O. Ramsay,
McGill University, Montreal, Canada

Titolo:
Estimating a Variance-Covariance Surface for Functional Data using 
Finite Elements

Abstract:
In functional data analysis, as in its multivariate counterpart, 
estimates of the bivariate covariance kernel sigma(s,t) and its inverse 
are useful for many things, and we need the inverse of a covariance 
matrix or kernel especially often.  However, the dimensionality of 
functional observations often exceeds the sample size available to 
estimate sigma(s,t).  Then the analogue of the multivariate sample 
estimate is singular and non-invertible.   Even when this is not the 
case, the high dimensionality of the usual estimate often implies 
unacceptable sample variability and loss of degrees of freedom for model 
fitting.   The common practice of employing low-dimensional principal 
component approximations to sigma(s,t) to achieve invertibility also 
raises serious issues.
This talk describes a functional and nonsingular estimate of sigma(s,t) 
and its inverse defined by an expansion in terms of finite element basis 
functions that permits the user to control the resolution of the 
estimate as well as the time lag over which covariance may be nonzero.   
This estimate also permits the estimation of covariances and 
correlations at observed pairs of sampling points, and therefore has 
applications to many classical statistical problems, such as discrete 
but unequally spaced time and spatial series.



Tutti gli interessati sono invitati a partecipare.


Cordiali saluti,
Laura Sangalli

-- 
Laura Maria Sangalli
MOX - Dipartimento di Matematica
Politecnico di Milano
Piazza Leonardo da Vinci 32
20133 Milano - Italy
tel: +39 02 2399 4554
fax: +39 02 2399 4606
email: laura.sangalli at polimi.it
url: http://mox.polimi.it/~sangalli
http://mox.polimi.it/~sangalli/firb.html