  This paper is concerned with model averaging estimation for partially linear
functional score models. These models predict a scalar response using both
parametric effect of scalar predictors and non-parametric effect of a
functional predictor. Within this context, we develop a Mallows-type criterion
for choosing weights. The resulting model averaging estimator is proved to be
asymptotically optimal under certain regularity conditions in terms of
achieving the smallest possible squared error loss. Simulation studies
demonstrate its superiority or comparability to information criterion
score-based model selection and averaging estimators. The proposed procedure is
also applied to two real data sets for illustration. That the components of
nonparametric part are unobservable leads to a more complicated situation than
ordinary partially linear models (PLM) and a different theoretical derivation
from those of PLM.
