Inference and Modeling with Log-concave Distributions
arXiv:1010.0305 · doi:10.1214/09-STS303
Abstract
Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible nonparametric class of distributions. Further, the MLE exists and can be computed with readily available algorithms. Thus, no tuning parameter, such as a bandwidth, is necessary for estimation. Due to these attractive properties, there has been considerable recent research activity concerning the theory and applications of log-concave distributions. This article gives a review of these results.
Published in at http://dx.doi.org/10.1214/09-STS303 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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- Nemirovski's Inequalities Revisited
- Multivariate Log-Concave Distributions as a Nearly Parametric Model
- A Bayesian nonparametric approach to log-concave density estimation
- Maximum-Likelihood Estimation of a Log-Concave Density based on Censored Data
- Log-concave density estimation in undirected graphical models
- Bimonotone Subdivisions of Point Configurations in the Plane