## Statistical Science

### Recent Progress in Log-Concave Density Estimation

Richard J. Samworth

#### Abstract

In recent years, log-concave density estimation via maximum likelihood estimation has emerged as a fascinating alternative to traditional nonparametric smoothing techniques, such as kernel density estimation, which require the choice of one or more bandwidths. The purpose of this article is to describe some of the properties of the class of log-concave densities on $\mathbb{R}^{d}$ which make it so attractive from a statistical perspective, and to outline the latest methodological, theoretical and computational advances in the area.

#### Article information

Source
Statist. Sci., Volume 33, Number 4 (2018), 493-509.

Dates
First available in Project Euclid: 29 November 2018

https://projecteuclid.org/euclid.ss/1543482055

Digital Object Identifier
doi:10.1214/18-STS666

Mathematical Reviews number (MathSciNet)
MR3881205

Zentralblatt MATH identifier
07032826

#### Citation

Samworth, Richard J. Recent Progress in Log-Concave Density Estimation. Statist. Sci. 33 (2018), no. 4, 493--509. doi:10.1214/18-STS666. https://projecteuclid.org/euclid.ss/1543482055

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