Study Of Interval Data

In reliability and survival analysis, the data obtained in modelling failure times are often interval censored. The exact occurrence time of an event is not observed, but what is known is the interval in which the event took place. They are generally named as interval censored data. When interval censoring arises, almost all traditional statistical methods cannot work any more.Recently there is an enormous amount of literature on interval censored data. In these studies, nonparametric likelihood estamation(NPMLE) are widely used in estimating distribution function or regression parameters.These estimators all have good asymptotic properties. Its limitation is that it is complicated to work out the likelihood functions and in most situations we can only use iterative operations to get an approximate solution. In this paper we will use unbiased transformation method to solve some estimating problems of interval censored data. Based on the observations we construct a series of 'new variables' to substitute the censored variable. These new variables have the same expectation as the censored variable. In this way many traditional statistical methods can be used again.In Chapter 1, We briefly review what is known about interval censored data and the nonparemetric likelihood estimation. Subsequently we introduce the unbiased transformation method. In Chapter 2, We estimate the rth original mement and variance of the censored variable and get a class of estimators having strong consistency (with the rate of O(n-1/2 (loglog n) 1/2)) and asymptotic normality. In Chapter 3. We estimate the variance of random error term in the linear regression model which allows the dependent variable to be interval-censored and the residual distribution to be unspecified. The estimators have good properties such as strong consistent and asymptotic normality. In Chanpter 4, We consider the nonparemetric regression model with the dependent variable to be interval-censored. After unbiased transformation, the nearest neighbour estimator of regression function is strongly consistent. In Chanpter 5, We consider the situations where the distribution of the censoring variables are unspecified. All above results are substantiated by simulations in Chanpter 6.