Regression model checking with Berkson measurement errors in covariates
Pei Geng, Illinois State University, USA
A minimum distance regression model checking approach is proposed when covariates are observed with Berkson measurement errors. When the measurement error density is unknown, it is assumed that validation data is available. This assumption makes it possible to estimate the calibrated regression function consistently. The proposed tests are based on a class of minimized integrated square distances between a nonparametric estimate of the calibrated regression function and the parametric null model being fitted. The asymptotic normality of these tests under the null hypothesis and the consistency against certain alternatives are established. A simulation study shows desirable performance of a member of the proposed class of estimators and tests.