  In this paper, we investigate the hypothesis testing problem that checks
whether part of covariates / confounders significantly affect the heterogeneous
treatment effect given all covariates. This model checking is particularly
useful in the case where there are many collected covariates such that we can
possibly alleviate the typical curse of dimensionality.
  In the test construction procedure, we use a projection-based idea and a
nonparametric estimation-based test procedure to construct an aggregated
version over all projection directions. The resulting test statistic is then
interestingly with no effect from slow convergence rate the nonparametric
estimation usually suffers from. This feature makes the test behave like a
global smoothing test to have ability to detect a broad class of local
alternatives converging to the null at the fastest possible rate in hypothesis
testing. Also, the test can inherit the merit of lobal smoothing tests to be
sensitive to oscillating alternative models. The performance of the test is
examined by numerical studies and the analysis for a real data example for
illustration.
