Linear Regression With Interval-Censored Covariate

In many areas of study, such as the modern industry, agriculture, medicine, economics, actuarial science, biological science and reliability engineering, the data for statistical inference and for the conduct of hypothesis testing and analysis, often can not be observed accurately. These observation data has been known either falls in a certain interval, or known to, be larger or smaller than a certain observation time point, we call these data censored or truncated. In recent years, the research of the censored data is paid great attention by statisticians, especially the research on the interval-censored data, is appearing in many area of study widely.In the study of interval-censored data, the study of regression model takes very important part. The statisticians make varied, effective methods of statistical inference study deeply and widely. However, these studies are often based on the assumption that the dependent variable is interval-censored data, while the independent variable is observed accurately. The conditions that when the independent variable is censored is not studied much by our statisticians. Guadalupe Gomez made great contributions to this area, where he has published a number of research results.Although the research on the explanatory variable for interval-censored data regression model is not much, such a study is necessary and urgent.This paper is based on Guadalupe Gomez's theoretical results and trying to make deeper discussion. In Guadalupe Gomez's papers, He had mainly concentrated on the condition that the independent variable was interval-censored, and the dependent variable was observed precisely. In this paper, I will continue to discuss when the independent variables are censored for a simple linear regression model, but expend the data type of the dependent and independent variables, analyze the situation when the dependent variable is right censored, then do the simulation test to verify the model.