A Bayesian nonparametric approach to log-concave density estimation

A Computational Approach to Log-Concave Density Estimation

Non-parametric density estimation with shape restrictions has witnessed a great deal of attention recently. We consider the maximumlikelihood problem of estimating a log-concave density from a given finite set of empirical data and present a computational approach to the resulting optimization problem. Our approach targets the ability to trade-off computational costs against estimation accuracy...

logcondens: Computations Related to Univariate Log-Concave Density Estimation

Maximum likelihood estimation of a log-concave density has attracted considerable attention over the last few years. Several algorithms have been proposed to estimate such a density. Two of those algorithms, an iterative convex minorant and an active set algorithm, are implemented in the R package logcondens. While these algorithms are discussed elsewhere, we describe in this paper the use of t...

Maximum likelihood estimation of a multi- dimensional log-concave density

Let X1, . . . ,Xn be independent and identically distributed random vectors with a (Lebesgue) density f. We first prove that, with probability 1, there is a unique log-concave maximum likelihood estimator f̂n of f. The use of this estimator is attractive because, unlike kernel density estimation, the method is fully automatic, with no smoothing parameters to choose. Although the existence proof ...

Nonparametric Regression Approach to Bayesian Estimation

Estimation of unknown parameters and functions involved in complex nonlinear econometric models is a very important issue. Existing estimation methods include generalised method of moments (GMM) by Hansen (1982) and others, efficient method of moments (EMM) by Gallant and Tauchen (1997), Markov chain Monte Carlo (MCMC) method by Chernozhukov and Hong (2003), and nonparametric simulated maximum ...

Categorization as nonparametric Bayesian density estimation 1 Running head: CATEGORIZATION AS NONPARAMETRIC BAYESIAN DENSITY ESTIMATION Categorization as nonparametric Bayesian density estimation