Statistical Inference On Restricted Linear Regression Models With Partial Distortion Measurement Errors

When we deal with the measurement error data, the naive procedure by simply ignoring measurement errors always leads to a biased and inconsistent estimator. As such, we should solve such practical problems by choosing relative measurement error models.There are two types of measurement error data. One has a multiplicative fashion, which we call distortion measurement error models. Another one is additive measurement error models, including the classical measurement error models. In this dissertation we consider the distortion measurement error models.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 parameter under some restricted conditions. Asymptotic properties for the estimator 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 analyzed for an illustration.