右删失数据下广义线性模型的统计诊断

Statistical Diagnostics for Generalized Linear Models with Right-Censored Data

研究了带有右删失数据的广义线性模型的统计诊断问题。首先构造了右删失数据下的似然函数,推导出了参数的极大似然估计。基于数据删除模型,推导出了数据删除前后参数估计的一阶近似公式,推广了广义Cook距离和似然距离等用来判定异常点或强影响点的诊断统计量,并证明了两者的等价性。最后通过实际数据分析,验证了该理论的正确性和实用性。

This paper investigates statistical diagnosis problem of the generalized linear models with right-censored data. First,we derive the likelihood function under right-censored data to obtain maximum likelihood estimates for the parameters. Based on the case-deletion models and using the first order Taylor approximation of parameter estimates,we then propose the diagnostic tools such as the generalized cook distance and the likelihood distance to determine outfielders and/or influential cases in the data. We also prove the equivalence of two distances. Finally,we use a real data example to verify the efficiency and feasibility of the proposed diagnostic methods.