SEMINARIO. Nils Hjort, University of Oslo: " Model averaging and focussed model selection criteria "Title: Istituto Metodi Quantitativi - Università L
Istituto Metodi
Quantitativi - Università L. Bocconi
Viale Isonzo, 25 - 20135 Milano Tel. 02-58365629 -
Fax 02-58365630 SEMINARIO Model
averaging and focussed model selection criteria Nils Hjort
Department of Mathematics, giovedì, 4 dicembre 2003 – ore 16.30 Aula IMQ – stanza 137 ___________________________________________________________________ Abstract . The traditional use of
model selection methods in practice is to proceed as if the final selected
model had been chosen in advance, without acknowledging the additional
uncertainty introduced by model selection. This often means underreporting of
variability and too optimistic confidence intervals. We build a general
large-sample likelihood apparatus in which limiting distributions and risk
properties of estimators-post-selection as well as of model average estimators
are precisely described, also explicitly taking modelling bias into account. This allows a drastic
reduction of complexity, as competing model averaging schemes may be developed,
discussed and compared inside a statistical prototype experiment where only a
few crucial quantities matter. In particular we offer a frequentist
view on Bayesian model averaging methods and give a link to generalised ridge
estimators. Our work also leads to new
model selection criteria. These are "focussed", in the sense that
they give different optimal models for different focus parameters -- the best
model for understanding the mean structure may not be the best model for
understanding the variance structure, for example. |