右删失数据下AFT-EV模型涵盖了AFT模型, EV模型以及删失数据等当下流行的统计因素, 其优点在于它继承了AFT模型易于解释的特点,且在实际中得到广泛应用, 又结合了EV模型的灵活性及T-型估计的稳健性优点.在医学、经济学、生物学、公共卫生学等很多领域都存在利用所观测的数据对某参数进行估计, 预测的问题, 而这些数据通常具有一个相同的特征, 即其中存在删失数据. 因此由于删失数据的普遍性, 所以我们有必要对右删失数据下的AFT模型进行讨论, 从而进一步增强模型的可应用性; 另外由于人为观测的失误, 或是仪器测量精度等原因, 使得我们实际获取的观测数据也难免会带有测量误差, 正是基于这些实际问题的考虑,本文提出了右删失数据下AFT-EV模型, 并研究了该模型的T-型估计问题.本文首先介绍了AFT模型, EV模型, 删失数据以及T-型估计的相关背景知识;其次利用EM算法推导出了模型中未知参数的估计, 并在适当的条件下, 证明了参数估计ˆ βn, ˆσn的相合性质以及渐近正态性; 最后通过计算机模拟对文中所提出的方法的可行性和估计结果的性质进行了验证, 并对不同的估计方法得出的估计进行了比较.

AFT-EV models with right censored data extensively cover many popular statistical elements such as AFT models,~EV models,right censored data and so on.~The advantages of the AFT-EV models lie in that they combine the merits of AFT models,~EV models and T-type estimate;~Firstly,~it is intuitively attractive and easily interpretable as the AFT models;~Secondly,~they show the flexible virtues as well as the EV models;~At last,~they have robust property because of the T-type estimate.~We should always use the observed data to estimate an unknown parameter or to forecast in many fields such as medicine,~economics,~biology,~School of Public Health.~These data are usually having the same characteristics:~ censored data.~Due to the universality of the censored data,~it is necessary for us to discuss the AFT models with right censored data to further enhance the applicability of the models;~At the same time,~due to the reasons such as observation mistakes and imprecise measurement of equipments,~we also have to deal with measurement error.~In summary,~base on the needs of those practical problems,~we put forward the AFT-EV models with right censored data and consider the T-type estimator of the models.~The first part of this article talks about the background knowledge of AFT models,~EV models,~censored data and T-type estimates;~then we propose the estimatesof the unknown parameters by EM Algorithm,~and the consistency and asymptotic normality of the estimators are proved under proper assumption.~Finally,~the finite-sample properties of the above methods are given by simulations which show the feasibility of the methods,~and comparisons are done between different methods.