Open Access
April 1996 Efficient estimation for the proportional hazards model with interval censoring
Jian Huang
Ann. Statist. 24(2): 540-568 (April 1996). DOI: 10.1214/aos/1032894452


The maximum likelihood estimator (MLE) for the proportional hazards model with "case 1" interval censored data is studied. It is shown that the MLE for the regression parameter is asymptotically normal with $\sqrt{n}$ convergence rate and achieves the information bound, even though the MLE for the baseline cumulative hazard function only converges at $n^{1/3}$ rate. Estimation of the asymptotic variance matrix for the MLE of the regression parameter is also considered. To prove our main results, we also establish a general theorem showing that the MLE of the finite-dimensional parameter in a class of semiparametric models is asymptotically efficient even though the MLE of the infinite-dimensional parameter converges at a rate slower than $\sqrt{n}$. The results are illustrated by applying them to a data set from a tumorigenicity study.


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Jian Huang. "Efficient estimation for the proportional hazards model with interval censoring." Ann. Statist. 24 (2) 540 - 568, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0859.62032
MathSciNet: MR1394975
Digital Object Identifier: 10.1214/aos/1032894452

Primary: 62E20 , 62G05
Secondary: 62G20 , 62P99

Keywords: Current status data , Information , interval censoring , maximum (profile) likelihood estimator , proportional hazards model , Semiparametric model

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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