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

In this dissertation, we mainly consider statistical inference for partial linear regression models when some variables are distorted with errors under linear restrictive condition.Partially linear regression model has found wildly applications. In this dissertation,we use non-parametric method in the estimation procedure, so the model we used also belongs to the category of semi-parametric model. Various semi-parametric regression models have been proposed to relax model assumptions imposed on traditional parametric models when dealing with real data, and also allow retaining the ease of interpretation of parameters in linear regression and the flexibility of a nonparametric model. In the last two decades, statistical analysis on the measurement error data has become one of the most important issues because measurement error data are often encountered in many fields, such as medicine, economics, engineering. As we know, 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, consequently, which promotes a continuous development of statistical research on the measurement error data. In this dissertation, we focus on the models with distortion measurement error.In this dissertation, we study parameter estimation and testing of partial linear models when the response and the covariates in the linear part are measured with errors and distorted by unknown distorting functions of one commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. Asymptotic properties for the estimator are established. Later, we investigate the estimation and testing of the partial linear regression model with measurement errors in parametric component based on linear restrictive condition. 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. It is shown that the test statistic is asymptotically distribution-free and follows a Chi-squared distribution. 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.