Efficient estimation of the partly linear additive Cox model
The Annals of Statistics · 1999 · Volume 27 · Issue 5
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.
Keywords
62G05, 62G07, 62G20, 62P99, additive regression, asymptotic normality, partial likelihood, polynomial splines, projection, rate of convergence, Right-censored data, semiparametric information bound
Enable JavaScript for citation tools and additional paper interactions.