Moment-type Estimation Of The Parameter Of Interval-censored Data

In survival analysis and reliability statistical study, due to some objectiveconditions, we can only observe the interval in which the event took place,but the accurate observation values can not often be obtained. Such datais generally named as interval-censored data on which a plenty ofresearch has been done. Interval censored data is applied in many areas,and its appearance adds much more difficulty to statistical analysis.However, the method of complete data cannot be applied directly to theinterval data, so it is very necessary to conduct some research on it.The present thesis is mainly on the moment-type estimation of theparameter of interval-censored data under arbitrary distribution and theasymptotic normality and consistency of estimator as well as to testify thefeasibility and availability of this estimation method adopted in this thesisby simulation. In particular, for the exponential distribution, comparedwith the previous method, the moment-type estimation is more effective.Further, this thesis tries to explore the hypothesis testing of the mean. It isfound that the process of using likelihood ratio testing method to test themean of interval-censored data is very complicated. If a relatively simpletesting method can be found, the testing problem of interval data willbecome simpler. Moreover, it is not only applicable to all distribution butalso the calculation process is very simple to test by estimator constructedby unbiased transformation.In the final, it involves a study to the distribution of the estimator Y,mainly the exponential distribution of the Case1interval-censored, andafterwards, the distribution functionH (ω)and density functionh (ω)aregiven.