A New Method Of Parameter Estimation For Interval-censored Data

In many branches of learning, such as medicine, biology, insurance, reliability engineering project science, public hygiene, economics, demographics etc, exist problems of estimating and forecasting the time of certain events occur. From the obtained data, these data have a common characteristic that the occurrence times of the event of interest are either censored or truncated, especially call it interval censored when we only know the event happens in certain time interval.As to the characteristic of interval-censored data, it is the estimation of the parameter of survival function this paper focuses on. By contrast, there are less research on parametric estimation under interval-censored data circumstances. In this paper, we summarize several methods to estimate the interval-censored data, such as midpoint(similarly, left or right extremes of interval) which ignore the interval-censored nature of the data and are too simple to make sense. The maximum likelihood estimation and is introduced as well.After studying the piecewise exponential model suggested by Jane C. Lindsey and Louise M. Ryan, I have mainly done three tasks. First, given the distribution family F is known ,take the conditional expectation of interval-censored data as its estimation so that the data can be treated as complete data in certain level. Second,combine the method with EM algorithm and programm in SAS software to solve the computational problem. The big sample property of the estimation proposed in this paper is discussed too. Last, by simulation I proved this method to be better and more efficient than some other method and can overcome the disadvantages in computing compared with some other method. In addition, this method can be further developed for interval-censored data with covariates.