Open Access
August 2016 Optimal estimation for the functional Cox model
Simeng Qu, Jane-Ling Wang, Xiao Wang
Ann. Statist. 44(4): 1708-1738 (August 2016). DOI: 10.1214/16-AOS1441


Functional covariates are common in many medical, biodemographic and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coefficient function for a functional covariate achieves the minimax optimal rate of convergence under a weighted $L_{2}$-risk. This optimal rate is determined jointly by the censoring scheme, the reproducing kernel and the covariance kernel of the functional covariates. Implementation of the estimation approach and the selection of the smoothing parameter are discussed in detail. The finite sample performance is illustrated by simulated examples and a real application.


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Simeng Qu. Jane-Ling Wang. Xiao Wang. "Optimal estimation for the functional Cox model." Ann. Statist. 44 (4) 1708 - 1738, August 2016.


Received: 1 January 2015; Revised: 1 January 2016; Published: August 2016
First available in Project Euclid: 7 July 2016

zbMATH: 1345.62028
MathSciNet: MR3519938
Digital Object Identifier: 10.1214/16-AOS1441

Primary: 62C20 , 62G05 , 62N01 , 62N02

Keywords: Cox models , functional data , minimax rate of convergence , partial likelihood , Right-censored data

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 4 • August 2016
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