Goodness-of-fit tests in linear EV regression with replications
The authors consider an error-in-variables linear regression model, i.e. the regressor \(X\) is observed via the surrogate \(Z = X + U\), i.e., besides the regression error there is the measurement error \(U\). The authors construct a goodness-of-fit test for the density function of the regression error under the assumption that the distribution of \(U\) is unknown. However, replications of the surrogates \(Z\) are available and are used to construct a nonparametric estimate of the density of \(U\). The test statistics is a weighted integrated squared distance between a nonparametric estimator and a semi-parametric estimator of the density functions of certain residuals. Asymptotic normality under the null hypothesis as well as consistency and local power results are proven. The finite sample behaviour is evaluated via simulation studies.
goodnes-of-fit test for error density functions
scientific article; zbMATH DE number 6887306
scientific article