A unified model specification for sparse and dense functional/longitudinal data

The semi varying-coefficient additive model is a flexible nonparametric regression method, including varying-coefficient model and additive model as its special cases. However, a complex model may lead over-fitting phenomenon, which motivates us to develop a set of testing procedure to judge whether a parsimonious submodel is sufficient or not. Specifically, we propose hypothesis testings to check time-varying property of varying-coefficient component functions and linearity of additive component functions, respectively. For repeated measurements data, it is a subjective choice between sparse and dense case, which may lead to wrong statistical inference. One major contribution of this paper is to introduce consistent testing methodologies in a unified framework of sparse, dense and ultra dense cases of the data, which avoids a subjective choice of data types in practical applications. Extensive Monte Carlo simulation studies investigating the finite sample performance of the proposed methodologies confirm our asymptotic results. We further illustrate our methodologies via two real-life data applications.