  Non-random sample selection is a commonplace amongst many empirical studies
and it appears when an output variable of interest is available only for a
restricted non-random sub-sample of data. We introduce an extension of the
generalized additive model which accounts for non-random sample selection by
using a selection equation. The proposed approach allows for different
distributions of the outcome variable, various dependence structures between
the (outcome and selection) equations through the use of copulae, and
nonparametric effects on the responses. Parameter estimation is carried out
within a penalized likelihood and simultaneous equation framework. We establish
asymptotic theory for the proposed penalized spline estimators, which extends
the recent theoretical results for penalized splines in generalized additive
models, such as those by Kauermann et al. (2009) and Yoshida & Naito (2014).
The empirical effectiveness of the approach is demonstrated through a
simulation study.
