## The Annals of Statistics

### Efficient estimation for the proportional hazards model with interval censoring

Jian Huang

#### Abstract

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

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

Dates
First available in Project Euclid: 24 September 2002

https://projecteuclid.org/euclid.aos/1032894452

Digital Object Identifier
doi:10.1214/aos/1032894452

Mathematical Reviews number (MathSciNet)
MR1394975

Zentralblatt MATH identifier
0859.62032

#### Citation

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. https://projecteuclid.org/euclid.aos/1032894452

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