Lack-of-fit testing in errors-in-variables regression model with validation data

A score-type test procedure is proposed for checking the adequacy of the errors-in-variables regression model when validation data are available. Under mild conditions, the score-type test statistic is proven to be asymptotically normal. The test procedure is shown to be consistent against general fixed alternatives and it can detect local alternatives which are close to the null model at the parametric rate. Monte-Carlo simulations are conducted to evaluated the finite sample performance of the proposed test.