An adaptive-to-model test for parametric single-index models with missing responses

This paper is devoted to implementing model checking for parametric single-index models with missing responses at random. Two dimension reduction adaptive-to-model tests applying to the missing responses situation are proposed. Unlike the existing smoothing tests, our methods can greatly alleviate the curse of dimensionality in the sense that the tests behave like a test with only one covariate. It results in better significance level maintenance and higher power than the classical tests. The finite sample performance is evaluated through several simulation studies and a comparison with other popularly used tests. A real data analysis is conducted for illustration.