Inference and Modeling with Log-concave Distributions

By Guenther Walther. 2009

118 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/eb401bbc87ca88bf7d6f58a8a63d9ae9734e0aa4

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Citations in the corpus

Efficient Robust Proper Learning of Log-concave Distributions (2016, methodology): “Log-concave distributions constitute a broad non-parametric family that is very useful for modeling and inference [Wal09].”
Differentially Private Learning of Structured Discrete Distributions (2015, background): “There is a long history of research in statistics on estimating structured families of distributions going back to the 1950’s [10, 11, 12, 13], and it is still a very active research area [14, 15, 16].”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, background): “Walther (2009) provides a nice recent review of inference and modelling with log-concave densities.”
Recent Progress in Log-Concave Density Estimation (2017, background): “For alternative reviews of related topics, see Saumard and Wellner (2014), which has a greater emphasis on analytic properties, and Walther (2009), with a stronger focus on modelling and applications.”
Smoothed log-concave maximum likelihood estimation with applications (2011, background): “Further properties of log-concave distributions are discussed in Schuhmacher, Hüsler and (2011), and Walther (2009) provides an overview of the field.”
APPROXIMATION BY LOG-CONCAVE DISTRIBUTIONS, WITH APPLICATIONS TO REGRESSION (2010, background): “Indeed, these distributions have received a lot of attention among statisticians recently as described in the review by Walther (2009).”
Log-Concavity and Strong Log-Concavity: a review (2014, methodology): “This particular family of densities on R was introduced in the context of binary mixed effects models by Wang and Louis [2003]. Example 2.”