Goodness-of-Fit Test in a Structural Errors-in-Variables Model Based on a Score Function

Abstract

A polynomial structural measurement error model is considered. A goodness-of-fit test is constructed based on the quasi-likelihood estimator, which is asymptotically optimal in a large class of estimators. The power of the test is discussed. The test for the linear model with unknown nuisance parameters is studied in more detail. Similar test can be applied to much more general situation, where the estimator is constructed based on a score function.