Statistical Inference On Quantileregression Models With Partial Distortion Measurement Errors

In recent years,with the rapid development of science and technology,we found that in more and more subjects,measurement errors appear frequently,in biomedical and health-related studies,the research and application of financial and engineering measure--ment and so on.There are two kinds of measurement error models: The first one is the measurement error data model with an additive form,including the traditional measurement error model as a special case.The other is the measurement error data model with a multiplication structure,which we call the distortion measurement error model.In this thesis,I mainly discuss the distortion measurement error model.Generally,this measurement error data model has the following features: first,the variables of interest are unobserved or can't be measured.Second,the main variables(response variables and covariates in the model)are distorted with errors by some unknown functions of commonly observable confounding variables.Therefore,the main research work of my paper is to build a quantile regression model for this kind of measurement data.When it comes to the data modeling of distortion measurement error data,there are a lot of studies which have given many quite valuable suggestions.My paper attempts to use a new model-quantile regression estimation to analyze this kind of data in order to achieve reasonable results.Asymptotic properties of the proposed estimators are established,and we also investigate the asymptotic relative efficiency compared with the least squares estimator.Finally,simulation studies are conducted to evaluate the performance of the proposed methods,and a real dataset is analyzed as an illustration.