Some Properties of A Lack-of-Fit Test for a Linear Errors in Variables Model

Abstract

The relationship between the linear errors-in-variables model and the corresponding ordinary linear model in statistical inference is studied. It is shown that normality of the distribution of covariate is a necessary and sufficient condition for the equivalence. Therefore, testing for lack-of-fit in linear errors-in-variables model can be converted into testing for it in the corresponding ordinary linear model under normality assumption. A test of score type is constructed and the limiting chi-squared distribution is derived under the null hypothesis. Furthermore, we discuss the power of the test and the choice of the weight function involved in the test statistic.

Model checking in errors-in-variables regression

“…For the errors-in-variables model, in the case of r (x) = x, Zhu, Cui and Ng [25] found a necessary and sufficient condition for the linearity of the conditional expectation E(ε|Z ) with respect to Z . Based on this fact, they constructed a score type lack-of-fit test.…”

An Adaptive-to-Model Test for Parametric Single-Index Errors-in-Variables Models

“…An alternative approach adopted in the literature is that of calibration, where the original regression relationship is transferred to the regression E(Y |W ) relationship between the response Y and the cohort W . Zhu et al (2004) established a sufficient and necessary condition for the linearity of E[Y |W ] with respect to W when g(β T 0 x, γ 0 ) = β T 0 x. A score-type lack-of-fitness test was proposed based on this fact.…”