An EM algorithm for density estimation with randomly censored data. (English) Zbl 1019.62033
Summary: We propose a new estimator of the probability density function when the data is randomly censored, obtained through an EM algorithm, for solving a “nonlinearly smoothed” maximum likelihood problem. This algorithm is based on setting the Gateaux derivatives, in all directions, of the smoothed likelihood function equal to zero. Simulation results are presented which suggest that the proposed estimator compares favorably to the Kaplan-Meier-based kernel density estimator.
MSC:
62G07 | Density estimation |
65C60 | Computational problems in statistics (MSC2010) |
References:
[1] | Acusta A., Nonparametric density estimation with randomly censored data (1998) |
[2] | Eggermont P., Applied Mathematics Optimisation 39 pp 75– (1999) · Zbl 0969.65122 · doi:10.1007/s002459900099 |
[3] | DOI: 10.1080/10485259508832613 · Zbl 1380.62144 · doi:10.1080/10485259508832613 |
[4] | DOI: 10.2307/2965415 · Zbl 0912.62054 · doi:10.2307/2965415 |
[5] | DOI: 10.1137/1114019 · doi:10.1137/1114019 |
[6] | DOI: 10.1007/BF02613509 · Zbl 0695.62105 · doi:10.1007/BF02613509 |
[7] | Johansen S., Scandinavian Journal of Statiitics 5 pp 195– (1978) |
[8] | DOI: 10.2307/2281868 · Zbl 0089.14801 · doi:10.2307/2281868 |
[9] | DOI: 10.2307/3315426 · Zbl 0849.60026 · doi:10.2307/3315426 |
[10] | DOI: 10.1080/03610928508828910 · Zbl 0566.62028 · doi:10.1080/03610928508828910 |
[11] | DOI: 10.1080/03610928408828780 · Zbl 0552.62021 · doi:10.1080/03610928408828780 |
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