Identification and estimation for generalized varying coefficient partially linear models

The generalized varying coefficient partially linear model (GVCPLM) enjoys the flexibility of the generalized varying coefficient model and the parsimony and interpretability of the generalized linear model. Statistical inference of GVCPLM is restricted with a condition that the components of varying and constant coefficients are known in advance. Alternatively, the current study is focused on the structure's identification of varying and constant coefficient for GVCPLM and it is based on the spline basis approximation and the group SCAD. This is proved that the proposed method can consistently determine the structure of the GVCPLM under certain conditions, which means that it can accurately choose the varying and constant coefficients precisely. Simulation studies and a real data application are conducted to assess the infinite sample performance of the proposed method.