The Annals of Statistics

Efficient estimation for the proportional hazards model with interval censoring

Jian Huang

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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.

Article information

Ann. Statist., Volume 24, Number 2 (1996), 540-568.

First available in Project Euclid: 24 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62E20: Asymptotic distribution theory
Secondary: 62G20: Asymptotic properties 62P99: None of the above, but in this section

Current status data interval censoring information maximum (profile) likelihood estimator proportional hazards model semiparametric model


Huang, Jian. Efficient estimation for the proportional hazards model with interval censoring. Ann. Statist. 24 (1996), no. 2, 540--568. doi:10.1214/aos/1032894452.

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