## Efficient estimation for the proportional hazards model with interval censoring.(English)Zbl 0859.62032

Summary: 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.

### MSC:

 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62P10 Applications of statistics to biology and medical sciences; meta analysis 62F12 Asymptotic properties of parametric estimators

NPSOL
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### References:

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