Maximum-likelihood estimation of a log-concave density based on censored data. (English) Zbl 1298.62062

Dümbgen, Lutz; Rufibach, Kaspar; Schuhmacher, Dominic

Electron. J. Stat. 8, No. 1, 1405-1437 (2014).

Summary: 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.

MSC:

62G07	Density estimation
62N02	Estimation in survival analysis and censored data
65C60	Computational problems in statistics (MSC2010)

Keywords:

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

Software:

Interval; R; survival; logconcens; logcondens

References:

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