Local Quasi-likelihood Estimation With Censoring Indicators Missing At Random

Survival analysis is a branch of applied statistics that has developed rapidly in recent years,which has been widely used in different fields.It is mainly a statistical method to study survival phenomena and response time data and their rules.The data of survival time is often incomplete,and censoring indicators missing at random is a relatively common phenomenon.Generalized linear model is an extension of linear regression model,and quasi-likelihood estimation is a kind of corresponding parameter estimation method,which is often used in survival analysisIn this paper,we consider the study of quasi-likelihood estimation when censoring indicators are missing at random,which is considering the observation data of {(Xi,Yi,?i?i,?i),1 ?i?n?,?i is the censoring indicator and ?i is the missing indictor that records whether the censoring indicator is missing.In combination with the construction method of the quasi?likelihood function under other complex data under generalized linear model,the estimation and properties of the quasi-likelihood method are studied when censoring indicators missing at random occurs.In the third chapter,we construct the complete data by imputation method,and construct the quasi-likelihood function by combining with the quasi-likelihood method under the complete data,also,we propose and prove the asymptotic property of the quasi-likelihood estimation.In addition,according to the above method,the influence factors on the life time of new subscribers with the censoring indicators missing at random in telecom industry are analyzed to verify the effectiveness of the method in practical application.Beyond that,based on the weighted quasi-likelihood method under complete data,we construct three weighted quasi-likelihood methods including calibration,imputation and inverse probability with the censoring indicators missing at random,and propose theorems and proof for the asymptotic properties of quasi-likelihood estimation.By constructing poisson's model,numerical simulation is carried out to further verify the asymptotic property of simulation effect and estimation.