The Statistical Properties Of Estimators In Ev Regression Model With Dependent Measurements

Regression analysis is a widely useful data analysis method. In practical applications, it is a very close to theory and practice of statistical method. Also it is an important tool to process and analyze relationships between research data. However, in practical problems, collecting data usually produce measurement errors. If we ignore these errors, the result estimators will be biased. To deal with these problems, measurement errors model becomes more realistic. Measurement errors model, i.e. EV regression model is the regression model that the covariate variable in the model has measurement errors.The main content of this paper is to study the asymptotic properties of the unknown parameters and errors variance in EV regression model with martingale difference error or negatively associated error. The whole paper is divided into five chapters:The first chapter is the introduction about the concept of martingale difference sequence, negatively associated sequence and EV regression model. We describe the background, significance of the study, and the literatures for EV regression model both domestic and foreign.The second chapter studies the EV linear regression model with martingale difference errors. Using the least squares estimation method to estimate unknown parameters in the model. Under certain conditions, we prove the strong consistency and mean square consistency of the estimators.The third chapter considers the estimation of a linear EV regression model under martingale difference errors. The usual least squares estimation usually leads to biased for estimators when measurement errors are ignored. By correcting the attenuation we propose a modified least squares estimator for a parametric component and construct the estimators of another parameter component and error variance. The asymptotic normality is also obtained for these estimators. The simulation study shows the modified least squares estimations perform better than the least squares estimations.The fourth chapter considers a semi-parametric EV regression model under negatively associated errors. For unknown parameter and unknown function, we both give their estimates. Under certain conditions, we obtained the strong consistencies of these estimators.The fifth chapter summarizes the full paper and presents next step plan and outlook.