Statistical Diagnostics For Generalized Linear Model With Censored Data

This paper mainly studies the statistical diagnosis problems of the generalized linear models under censored data.We focus on two types of censored data including left-censored data and right-censored data.First,we derive the likelihood function of the model under different censored data,and use the method of maximum likelihood estimation to obtain the parameter estimation.Based on the case-deletion models and mean-shift outlier models,the first-order Taylor approximation of the parameter estimation is derived and the equivalence of the two models is proved.Then we propose the diagnostic statistics such as the generalized leverage,the generalized cook distance,the likelihood distance and score statistics which are used to determine outliers,influential cases and high leverage points in the data.Next the local influence analysis based on likelihood distance of the model is carried out,and the simple calculation formula of the influence matrix is given by using the dependent variable perturbation model.Finally,we use a real data example to find outliers,influential cases and high leverage points in the data which verifies the correctness and practicability of the proposed diagnostic methods.