Statistics Group
Research Seminar
Maximum likelihood estimation
of a multidimensional log-concave density
Dr Richard Samworth
Department of Pure Mathematics
and Mathematical Statistics
University of Cambridge
Friday 14th November 2008
11.00am
Room Q229, M Block
Abstract
We show that if X1, …, Xn are a random sample from a log-concave density f in
Rd, then with probability one there exists a unique maximum likelihood
estimator fn* of f. The use of this estimator is attractive because, unlike kernel
density estimation, the estimator is fully automatic, with no smoothing
parameters to choose.
We exhibit an iterative algorithm for computing the estimator and show how
the method can be combined with the EM algorithm to fit finite mixtures of logconcave densities. The talk will be illustrated with pictures from the R package
LogConcDEAD. I also hope to discuss some recent results on the theoretical
performance of the estimator.
This is joint work with Madeleine Cule (Cambridge), Bobby Gramacy
(Cambridge) and Michael Stewart (University of Sydney).
*Everyone Welcome*
Tea and coffee will be available from 10.30am