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Estimators for the interval censoring problem. (English) Zbl 1271.62098

Summary: We study three estimators for the interval censoring case 2 problem, a histogram-type estimator, proposed in [L. Birgé, Math. Methods Stat. 8, No. 3, 285–298 (1999; Zbl 1033.62033)], the maximum likelihood estimator (MLE) and the smoothed MLE, using a smoothing kernel. Our focus is on the asymptotic distribution of the estimators at a fixed point. The estimators are compared in a simulation study.

MSC:

62G20 Asymptotic properties of nonparametric inference
62N01 Censored data models
60F05 Central limit and other weak theorems

Citations:

Zbl 1033.62033
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References:

[1] Lucien Birgé, Interval censoring: a nonasymptotic point of view , Math. Methods Statist. 8 (1999), no. 3, 285-298. · Zbl 1033.62033
[2] R. B. Geskus and P. Groeneboom, Asymptotically optimal estimation of smooth functionals for interval censoring. I , Statist. Neerlandica 50 (1996), no. 1, 69-88. · Zbl 0856.62039 · doi:10.1111/j.1467-9574.1996.tb01481.x
[3] R. B. Geskus and P. Groeneboom, Asymptotically optimal estimation of smooth functionals for interval censoring. II , Statist. Neerlandica 51 (1997), no. 2, 201-219. · Zbl 0891.62033 · doi:10.1111/1467-9574.00050
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