Statistical Science

Inference and Modeling with Log-concave Distributions

Guenther Walther

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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.

Article information

Source
Statist. Sci. Volume 24, Number 3 (2009), 319-327.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
http://projecteuclid.org/euclid.ss/1270041258

Digital Object Identifier
doi:10.1214/09-STS303

Mathematical Reviews number (MathSciNet)
MR2757433

Zentralblatt MATH identifier
1329.62192

Keywords
Nonparametric density estimation shape constraint log-concave density Polya frequency function strongly unimodal iterative convex minorant algorithm active set algorithm

Citation

Walther, Guenther. Inference and Modeling with Log-concave Distributions. Statist. Sci. 24 (2009), no. 3, 319--327. doi:10.1214/09-STS303. http://projecteuclid.org/euclid.ss/1270041258.


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