AVVISO DI SEMINARIO

[Carlo Gaetan <gaetan@stat.unipd.it>]

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                 DIPARTIMENTO DI SCIENZE STATISTICHE
		   Via S. Francesco, 33 - 35121 Padova
			tel. 0498274168


Il Prof. Nils Lid Hjort
Department of Mathematics
UNIVERSITY OF OSLO

terrą il seguente seminario:

MAXIMUM SIMULATED LIKELIHOOD ESTIMATORS

4 Ottobre 2000
ore 11.30-12.30
Aula B2, Ca' Borin

Summary
Suppose summary statistics $T=(T_1,\ldots,T_p)$ have 
been observed, perhaps computed from a difficult raw data set,
and that it is required to fit a certain model to these, 
parameterised by $\theta=(\theta_1,\ldots,\theta_d)$,
where $p\ge d$. I focus here on cases where the complexities 
of the model or of the data collection make it impossible to 
calculate the likelihood $L_T(\theta)$. I propose a simulation-based
method for approximating $\theta^*$, the ML estimator based on $T$.
It consists in simulating many realisations $T^*$ for many 
values of $\theta$, and then using techniques of density estimation 
and nonparametric regression to estimate the real maximiser
of $L_T(\theta)$. Similarly Bayes estimators may be approximated
via simulations. 

Using such methods one may in principle approximate ML estimators 
in any parametric models, as long as it is possible to simulate 
realisations of the $T$ in question from any given parameter value. 
In particular, ML estimators may be computed without deriving 
or caring about formulae for the likelihood or its derivatives
at all. Estimation uncertainty may also be addressed, via parametric
boostrapping. 

Illustrations of the technique will be given.


Cordiali saluti,
Carlo Gaetan









Carlo GAETAN                               e-mail:gaetan@stat.unipd.it
Dipartimento di Scienze Statistiche        phone : ++39-049-827-41-68
Via S. Francesco, 33                               ++39-049-827-41-80  (desk)
I-35121 PADOVA                             fax   : ++39-049-87-53-930
   ITALY