Abstract: In testing the adequacy of a regression model, the conditional expectation of the residuals given the observed covariate is often employed to construct lack-of-fit tests. However, in the errors-in-variables model, the resiudal is biased and cannot be used directly. In this paper, by correcting for the bias, we suggest lack-of-fit tests of score type for a general linear errors-in-variables model. The polynomial model is a special case. The tests are asymptotically chi-squared under the null hypothesis. The choice of scores involved in the test statistics and the power properties are investigated. A simulation study shows that the tests perform well. Application to two data sets is also made. The approach can readily be extended to handle general parametric models.
Key words and phrases: Bias correction, errors-in-variables model, lack-of-fit test.