Date: 2013-04-05
Time: 14:30-15:30
Location: BURN 1205
Abstract:
We consider the problem of predictive density estimation under Kullback-Leibler loss when the parameter space is restricted to a convex subset. The principal situation analyzed relates to the estimation of an unknown predictive p-variate normal density based on an observation generated by another p-variate normal density. The means of the densities are assumed to coincide, the covariance matrices are a known multiple of the identity matrix. We obtain sharp results concerning plug-in estimators, we show that the best unrestricted invariant predictive density estimator is dominated by the Bayes estimator associated with a uniform prior on the restricted parameter space, and we obtain minimax results for cases where the parameter space is (i) a cone, and (ii) a ball. A key feature, which we will describe, is a correspondence between the predictive density estimation problem with a collection of point estimation problems. Finally, if time permits, we describe recent work concerning : (i) non-normal models, and (ii) analysis relative to other loss functions such as reverse Kullback-Leibler and integrated L2.
References.
- Dominique Fourdrinier, Éric Marchand, Ali Righi, William E. Strawderman. On improved predictive density estimation with parametric constraints, Electronic Journal of Statistics 2011, Vol. 5, 172-191.
- Tatsuya Kubokawa, Éric Marchand, William E. Strawderman, Jean-Philippe Turcotte. Minimaxity in predictive density estimation with parametric constraints. Journal of Multivariate Analysis, 2013, Vol. 116, 382-397.
Speaker
Éric Marchand is a Professor of Statistics at the Université de Sherbrooke.