## The Annals of Statistics

### Maximum smoothed likelihood estimators for the interval censoring model

Piet Groeneboom

#### Abstract

We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show that, under smoothness conditions on the underlying distributions and using the usual bandwidth choice in density estimation, the local convergence rate is $n^{-2/5}$ and the limit distribution is normal, in contrast with the rate $n^{-1/3}$ of the ordinary maximum likelihood estimator.

#### Article information

Source
Ann. Statist. Volume 42, Number 5 (2014), 2092-2137.

Dates
First available in Project Euclid: 11 September 2014

https://projecteuclid.org/euclid.aos/1410440635

Digital Object Identifier
doi:10.1214/14-AOS1256

Mathematical Reviews number (MathSciNet)
MR3262478

Zentralblatt MATH identifier
1305.62142

Subjects
Primary: 62G05: Estimation 62N01: Censored data models
Secondary: 62G20: Asymptotic properties

#### Citation

Groeneboom, Piet. Maximum smoothed likelihood estimators for the interval censoring model. Ann. Statist. 42 (2014), no. 5, 2092--2137. doi:10.1214/14-AOS1256. https://projecteuclid.org/euclid.aos/1410440635

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