Open Access
2014 Maximum-likelihood estimation of a log-concave density based on censored data
Lutz Dümbgen, Kaspar Rufibach, Dominic Schuhmacher
Electron. J. Statist. 8(1): 1405-1437 (2014). DOI: 10.1214/14-EJS930


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.


Download Citation

Lutz Dümbgen. Kaspar Rufibach. Dominic Schuhmacher. "Maximum-likelihood estimation of a log-concave density based on censored data." Electron. J. Statist. 8 (1) 1405 - 1437, 2014.


Published: 2014
First available in Project Euclid: 20 August 2014

zbMATH: 1298.62062
MathSciNet: MR3263127
Digital Object Identifier: 10.1214/14-EJS930

Primary: 62G07 , 62N01 , 62N02 , 65C60

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

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
Back to Top