Journal
STATISTICAL SCIENCE
Volume 24, Issue 3, Pages 319-327Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/09-STS303
Keywords
Nonparametric density estimation; shape constraint; log-concave density; Polya frequency function; strongly unimodal; iterative convex minorant algorithm; active set algorithm
Categories
Funding
- NSF [DMS-05-05682]
- NIH [1R21AI069980]
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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.
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