Integrated conditional moment test for partially linear single index models incorporating dimension-reduction

Studying model checking problems for partially linear singleindex models, we propose a variant of the integrated conditional moment test using a linear projection weighting function, which gains dimension reduction and makes the proposed method act as if there exists only one covariate even in the presence of multiple dimensional regressors. We derive asymptotic distributions of the proposed test; i.e., an integral of a Ma’s research was supported by NSF grant DMS 1306972. Zhang’s research wa supported by Natural Science Foundation of SZU (801, 00036112), the NSFC (Tianyuan fund for Mathematics, NO.11326179) of China, and NSFC grant 11101157 of China. Sun’s research was supported by the President Fund of University of Chinese Academy of Sciences. Corresponding author. Liang’s research was partially supported by NSF grants DMS1007167 and DMS-1207444, and by Award Number 11228103, made by National Natural Science Foundation of China.