  In this paper we propose a generalized Gaussian process concurrent regression
model for functional data where the functional response variable has a
binomial, Poisson or other non-Gaussian distribution from an exponential family
while the covariates are mixed functional and scalar variables. The proposed
model offers a nonparametric generalized concurrent regression method for
functional data with multi-dimensional covariates, and provides a natural
framework on modeling common mean structure and covariance structure
simultaneously for repeatedly observed functional data. The mean structure
provides an overall information about the observations, while the covariance
structure can be used to catch up the characteristic of each individual batch.
The prior specification of covariance kernel enables us to accommodate a wide
class of nonlinear models. The definition of the model, the inference and the
implementation as well as its asymptotic properties are discussed. Several
numerical examples with different non-Gaussian response variables are
presented. Some technical details and more numerical examples as well as an
extension of the model are provided as supplementary materials.
