Multiple Imputation Of Censored Data In Quantile Regression

In many practical problems,because there is a constraint subjective and objective conditions,the observed data we get are always not accurate data,and sometimes only the data of interest to know the value of some of the data set is less than(greater than)or equal to a certainvalue or interposed within a certain range segment,we call this incomplete data censored data(Censored Observation).There are different types of censored data,such as left censoring,right censoring and interval censoring.In addition,the censored data can be divided into fixed censoring and random censoring.In the late of 1970s,for the above incomplete data,Dempster,Laird and Rubin(1977)presents a valid estimation of the EM algorithm.On the basis of this algorithm,Rubin(1977)proposed the idea of multiple imputation by simulating incomplete data.Since then,Rubin published a series of articles in this area,and later to organize and published in book form in 1987,he systematically summed up the ideological and theoretical framework of multiple imputation.In addition,quantile regression model provides a semi-parametric method that can flexibly handle the relationship between covariates and response variables.Even it provides a natural way to model data with heterogeneity.So far,the research of combining quantile regression with incomplete data is not a well-developed field.But the case of quantile regression for the response variable which is censored can be said to be very suitable.Because there is no strict parameters on the distribution assumptions in quantile regression,the conditional mean function is not recognized.In this dissertation,when the response variable is subject to a fixed censoring,we propose a new method that will combine quantile regression and multiple imputation to impute the censored data.The end result will be made some appropriate comparison,we found that the use of the results obtained by the method is in line with expectations.The main purpose of this paper is to propose a new approach to incorporate the censored data and impute them,and increase the efficiency of estimation.The main structure of the whole dissertation is as follows:In Chapter 1,we introduce the research background,significance and literature review,and advise the structure of this article,that is the study of the ideas and the framework.the other is the main innovation of this article.In Chapter 2,we introduce the basic concepts of quantile and the concepts of quantile regression,its parameter estimation methods and the assessment tests.Then we introduce the theory and properties of the censored quantile regression(CQR).Finally,it focuses on some theoretical basis of multiple imputation method.In Chapter 3,we will introduce a new algorithm for impute the censored data of the response variable.Firstly we present the basic theory associated with this algorithm,and use it for a variety of fixed-censored data to simulate the situation,and detailedly analysis the results of the simulation.In Chapter 4,we will present a example of methods used under the actual data,and the results were appropriately analysed.In Chapter 5,we summarize our proposed algorithm,and put forward our shortcomings and the prospect of the method.