Consistent model checking procedures for parametric regressions with missing response

Abstract

In this article, we introduce two new test statistics based on pairwise distance to check whether a parametric model with missing response is correctly specified or not. The proposed test statistics are easy to implement and no non parametric function estimation is involved. The asymptotic properties of the newly introduced test statistics are investigated. Under the null hypothesis, it is shown that they converge to a non degenerate distribution. And it can also detect any local alternatives that are different from the null at the parametric rate. In addition, the convergence rates of the proposed test are unaffected by the dimension of covariates. Some simulation studies and a real data example are conducted to show the good performance of the proposed test.