Journal
ANNALS OF STATISTICS
Volume 44, Issue 4, Pages 1708-1738Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/16-AOS1441
Keywords
Cox models; functional data; minimax rate of convergence; partial likelihood; right-censored data
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Funding
- NSF [DMS-09-06813, CMMI-1030246, DMS-10-42967]
- Direct For Mathematical & Physical Scien [1228369] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1228369] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1512975] Funding Source: National Science Foundation
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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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