Estimation Of Parameters Under Iterval-Censored Covariate Regression Model

In many branches of learning, such as medicine, biology, insurance, reliability engineering project science, public hygiene, economics, demographics etc, Interval-censored observations of a response variable are a common occurrence. and usually result when the response is the elapsed time until some event whose occurrence is periodically monitored.In this paper we consider a linear regression model in which the covariate variable is interval censored. By contrast, there are less research on this issue. we summarize several methods such as taking the midpoint of the interval-censored covariate and applying ordinary least-squares, but it is not in general valid. In 2003 Gomez use a likelihood approach, together with a two-step conditional algorithm, to jointly estimate the regression coefficients , but as a iteration algorithm ,it is too complicated to use.As to this issue, After studying article[12],I have mainly done four tasks to deal with linear regression analysis under interval censored covariate. First, By constructing conditional mean of the interval censored covariate, the estimators of regression parameters are obtained. Second, we prove the unbiasness and consistency of the estimators when the distribution of covariate is given. Third, We discuss the semi-parametric regression model under interval censored covariate. Forth, Simulation. The simulation results indicate that our method is easy to use than Gomez's approach and performs very good in terms of the accuracies of the estimation.