## The Annals of Statistics

### Efficient estimation of the partly linear additive Cox model

Jian Huang

#### Abstract

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

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

Dates
First available in Project Euclid: 23 September 2004

https://projecteuclid.org/euclid.aos/1017939141

Digital Object Identifier
doi:10.1214/aos/1017939141

Mathematical Reviews number (MathSciNet)
MR2000m:62015

Zentralblatt MATH identifier
0977.62035

#### Citation

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

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• IOWA CITY, IOWA 52242 E-MAIL: jian@stat.uiowa.edu