  We investigate the issue of bandwidth estimation in a nonparametric
functional regression model with function-valued, continuous real-valued and
discrete-valued regressors under the framework of unknown error density.
Extending from the recent work of Shang (2013, Computational Statistics & Data
Analysis), we approximate the unknown error density by a kernel density
estimator of residuals, where the regression function is estimated by the
functional Nadaraya-Watson estimator that admits mixed types of regressors. We
derive a kernel likelihood and posterior density for the bandwidth parameters
under the kernel-form error density, and put forward a Bayesian bandwidth
estimation approach that can simultaneously estimate the bandwidths. Simulation
studies demonstrated the estimation accuracy of the regression function and
error density for the proposed Bayesian approach. Illustrated by a spectroscopy
data set in the food quality control, we applied the proposed Bayesian approach
to select the optimal bandwidths in a nonparametric functional regression model
with mixed types of regressors.
