The Annals of Statistics

Efficient estimation of the partly linear additive Cox model

Jian Huang

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The partly linear additive Cox model is an extension of the (linear) Cox model and allows flexible modeling of covariate effects semiparametrically. We study asymptotic properties of the maximum partial likelihood estimator of this model with right-censored data using polynomial splines. We show that, with a range of choices of the smoothing parameter (the number of spline basis functions) required for estimation of the nonparametric components, the estimator of the finite-dimensional regression parameter is root-$n$ consistent, asymptotically normal and achieves the semiparametric information bound. Rates of convergence for the estimators of the nonparametric components are obtained. They are comparable to the rates in nonparametric regression. Implementation of the estimation approach can be done easily and is illustrated by using a simulated example.

Article information

Ann. Statist., Volume 27, Number 5 (1999), 1536-1563.

First available in Project Euclid: 23 September 2004

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties
Secondary: 62G07: Density estimation 62P99: None of the above, but in this section

Additive regression asymptotic normality right-censored data partial likelihood polynomial splines projection rate of convergence semiparametric information bound


Huang, Jian. Efficient estimation of the partly linear additive Cox model. Ann. Statist. 27 (1999), no. 5, 1536--1563. doi:10.1214/aos/1017939141.

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