Recent progress in log-concave density estimation

TL;DR

This paper reviews recent advances in log-concave density estimation, highlighting its advantages over traditional methods, and discusses new methodological, theoretical, and computational developments in the field.

Contribution

It provides a comprehensive overview of the properties and recent progress in log-concave density estimation, emphasizing its statistical appeal and recent innovations.

Findings

Log-concave densities have attractive statistical properties.

Recent methods improve estimation accuracy and computational efficiency.

Theoretical results support the robustness of log-concave estimators.

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.