Hypothesis tests in partial linear errors-in-variables models with missing response

In this paper, we investigate the problem of testing nonparametric function in partial linear errors-in-variables models with response missing at random. In order to overcome the bias produced by measurement errors, two bias-corrected test statistics based on the quadratic conditional moment method are proposed. The limiting null distributions of the test statistics are established respectively and p values can be easily determined which show that the proposed test statistics have similar theoretical properties. Moreover, our tests can detect the alternatives distinct from the null hypothesis at the optimal nonparametric rate for local smoothing-based methods in this area. Simulation studies are conducted to demonstrate the performance of the proposed test methods and the proposed two tests give similar performances. A real data set from the ACTG 175 study is used for illustrating the proposed test methods.