Maximum-Likelihood Estimation of a Log-Concave Density based on Censored Data

Lutz Duembgen; Kaspar Rufibach; Dominic Schuhmacher

doi:10.1214/14-ejs930

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arXiv · 1311.6403

Maximum-Likelihood Estimation of a Log-Concave Density based on Censored Data

Lutz Duembgen·Kaspar Rufibach·Dominic Schuhmacher

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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.

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BibTeX RIS

Lutz Duembgen, Kaspar Rufibach, Dominic Schuhmacher. 2014-07-28. Maximum-Likelihood Estimation of a Log-Concave Density based on Censored Data. https://doi.org/10.1214/14-ejs930

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