Statistical inference on restricted linear regression models with partial distortion measurement errors

Abstract

We consider statistical inference for linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variables. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed for unknown parameters under some restricted conditions. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for an illustration.