  We propose a functional accelerated failure time model to characterize
effects of both functional and scalar covariates on the time to event of
interest, and provide regularity conditions to guarantee model identifiability.
For efficient estimation of model parameters, we develop a sieve maximum
likelihood approach where parametric and nonparametric coefficients are bundled
with an unknown baseline hazard function in the likelihood function. Not only
do the bundled parameters cause immense numerical difficulties, but they also
result in new challenges in theoretical development. By developing a general
theoretical framework, we overcome the challenges arising from the bundled
parameters and derive the convergence rate of the proposed estimator.
Furthermore, we prove that the finite-dimensional estimator is
$\sqrt{n}$-consistent, asymptotically normal and achieves the semiparametric
information bound. The proposed inference procedures are evaluated by extensive
simulation studies and illustrated with an application to the sequential organ
failure assessment data from the Improving Care of Acute Lung Injury Patients
study.
