title: Maximum likelihood estimation of the mixture of log-concave densities.
abstract: Finite mixture models are useful tools and can be estimated via the EM algorithm. A main drawback is the strong parametric assumption about the component densities. In this paper, a much more flexible mixture model is considered, which assumes each component density to be log-concave. Under fairly general conditions, the log-concave maximum likelihood estimator (LCMLE) exists and is consistent. Numeric examples are also made to demonstrate that the LCMLE improves the clustering results while comparing with the traditional MLE for parametric mixture models.
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.
authors.forename: Hao
authors.initials: H
authors.lastname: Hu
authors.affiliation: Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.
authors.forename: Yichao
authors.initials: Y
authors.lastname: Wu
authors.affiliation: Department of Statistics, University of California, Riverside, California 92521, U.S.A.
authors.forename: Weixin
authors.initials: W
authors.lastname: Yao
keywords: Consistency; Log-concave maximum likelihood estimator (LCMLE); Mixture model