On Global Optimization of the Likelihood Function for Linear Time Series
Models
*Tuesday 5 June 2018*
*Venue:* Department of Mathematics, via Sommarive, 14 - Povo (TN) - Seminar
Room "-1"
*At: *4:30 pm
Speaker:
- *Bernard Hanzon* (Dept Mathematics, University College Cork, Ireland)
*Abstract:*
We present an approach to find the global optimum of a linear time series
model in state space form. By firstly applying a partial optimization step
to the likelihood function the problem can be reduced to a problem of
optimization of the likelihood over a set which has compact closure. By
applying a regularization the resulting problem is that of finding the
optimum of a Lipschitz continuous function on a compact set which is known
to have a (constructive) solution. Techniques from the theory of
parametrization of linear state space systems and some basic techniques
from differentiable manifold theory are used to obtain these results.
Furthermore the surprising fact is shown that the "crude" maximum
likelihood estimator (without regularization and compactification) does not
exist in the sense that the likelihood function has an infinite, typically
unattained, supremum. Comments will be made about the effect of the
regularization used on the outcome.
*Contact person: *Stefano Bonaccorsi