## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 8, Number 1 (2014), 1405-1437.

### Maximum-likelihood estimation of a log-concave density based on censored data

Lutz Dümbgen, Kaspar Rufibach, and Dominic Schuhmacher

#### Abstract

We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a subprobability density with an additional mass at $+\infty$, which is estimated simultaneously. The existence of the estimator is proved under mild conditions and various theoretical aspects are given, such as certain shape and consistency properties. An EM algorithm is proposed for the approximate computation of the estimator and its performance is illustrated in two examples.

#### Article information

**Source**

Electron. J. Statist. Volume 8, Number 1 (2014), 1405-1437.

**Dates**

First available in Project Euclid: 20 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1408540292

**Digital Object Identifier**

doi:10.1214/14-EJS930

**Mathematical Reviews number (MathSciNet)**

MR3263127

**Zentralblatt MATH identifier**

1298.62062

**Subjects**

Primary: 62G07: Density estimation 62N01: Censored data models 62N02: Estimation 65C60: Computational problems in statistics

**Keywords**

Active set algorithm binning cure parameter expectation-maximization algorithm interval-censoring qualitative constraints right-censoring

#### Citation

Dümbgen, Lutz; Rufibach, Kaspar; Schuhmacher, Dominic. Maximum-likelihood estimation of a log-concave density based on censored data. Electron. J. Statist. 8 (2014), no. 1, 1405--1437. doi:10.1214/14-EJS930. https://projecteuclid.org/euclid.ejs/1408540292