| 讲座简介： | The classic integrated conditional moment (ICM) test is a promising method for model check- 10 ing and its basic idea has been applied to develop several variants. However, in diverging dimension scenarios, the ICM test may break down and has completely different limiting properties from those in fixed dimension cases, and the related wild bootstrap approximation would also be invalid. To extend the ICM test to diverging dimension settings, we propose a projected adaptiveto-model version of the ICM test. We study the asymptotic properties of the new test under both 15 the null and alternative hypotheses to examine its ability of significance level maintenance and its sensitivity to the global and local alternatives that are distinct from the null at the rate n −1/2 . The corresponding wild bootstrap approximation can still work in diverging dimension scenarios. We also derive the consistency and asymptotically linear representation of the least squares estimator of the parameter at the fastest rate of divergence in the literature for nonlinear models. 20 The numerical studies show that the new test can greatly enhance the performance of the ICM test in high-dimensional cases. We also apply the test to a real data set for illustration. |
