Three Parameter Weibull Moment Estimation And Empirical Likelihood Statistics Inference For Interval Censored Data

Survival analysis is a subject that studies survival phenomena and response time data and their statistical rules.The subject has important applications in biology,medicine,insurance,reliability engineering,demography,sociology,economic and so on.The main data type in survival analysis is censored data,which means that the observed data are not continuous,but there are blank segments.Interval censored data,as one of the most important types of censored data,has many forms,and has a wide range of existence and application in real life.This paper mainly studies the estimation of three-parameter Weibull distribution moments under interval censored data and empirical likelihood statistical inference of partial linear models under interval censored data,including:In the first part,under the condition of interval censored data,the moment estimation equation of three-parameter Weibull distribution under interval censored data is obtained by using the mean residual life function in survival analysis to construct sample moments.We proved the consistency of this method and have done a lot of simulation research.The deviation and mean square error of moment estimation parameters are obtained.From the results,it can be seen intuitively that with the increase of sample size,the deviation and mean square error will decrease.It shows that the method has good unbiasedness,robustness and consistency.In the second part,the unbiased transformation method is used to transform the type of interval censored data into complete data,and then the empirical likelihood statistical method is used to estimate the parameters by selecting partial linear models.The kernel estimation is used to eliminate the partial linear problem,and the chi-square asymptotic property of the empirical likelihood equation is proved,and the parameter coverage is obtained.From the results,we can see that with the increase of sample size,the coverage becomes higher and higher,and the fitting effect of QQ plot is better.The QQ plot of 500 samples is given,which shows that it is feasible to use partial linear model to solve the problem of interval censored data.