  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.
