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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: Maximum likelihood estimation of a multidimensional log-concave density

Presented by Richard Samworth, University of Cambridge

13 February 2009 14:00 in CM221

We show that if $X_1,...,X_n$ are a random sample from a log-concave density $f$ in $\mathbb{R}^d$, then with probability one there exists a unique maximum likelihood estimator $\hat{f}_n$ 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 log-concave densities. Applications to classifcation, clustering and functional estimation problems will be discussed, and the talk will be illustrated with pictures from the R package LogConcDEAD.

Co-authors: Madeleine Cule (University of Cambridge), Robert Gramacy
(University of Cambridge) and Michael Stewart (University of Sydney).

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