具有随机回归子的不完全信息和随机截尾的广义线性模型的重对数律

摘要

In the reliability study,the randomly censored linear model (RCLM) with incomplete information is often concerned.In the present paper,we generalize the RCLM to the randomly censored generalized linear model with stochastic regressors and incomplete information and study the convergence rate of the maximum likelihood estimate (MLE) on the latter in the probability limit theory and attain two iterated logarithm laws.The first one gives in an asymptotic sense the smallest 100％ confidence interval for the parameter,while the second one gives an almost sure lower bound on the accuracy that the estimator can achieve.%在可靠性研究中,带有不完全信息随机截尾的线性模型经常受到关注.本文将带有不完全信息随机截尾的线性模型推广到带有随机回归子的不完全信息的随机截尾广义线性模型,并运用概率极限理论对后者的极大似然估计的收敛速度进行了研究,得到了两个重对数律.从渐近的意义看,第一个重对数律给出了未知参数的最小100％置信区间,而第二个重对数律给出了估计量能够达到的精确下界.