“…This is because nonparametric estimationbased methods rely on local smoothing techniques and empirical process-based tests are the averages of functions of weighted sum of residuals over an index set, which is a global smoothing step. Zhu and Li (1998) and Lavergne and Patilea (2012), are based on nonparametric estimation for the conditional moment and thus belongs to the class of local smoothing methods. Guo et al (2016) introduced an adaptive-to-model test that is based on Zheng (1996).…”