Inference and Modeling with Log-concave Distributions

Guenther Walther

doi:10.1214/09-sts303

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arXiv · 1010.0305

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.

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Guenther Walther. 2010-10-02. Inference and Modeling with Log-concave Distributions. https://doi.org/10.1214/09-sts303

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