不完全数据下半参数单调转移模型的统计推断及其应用

Incomplete data widely exist in many fields such as biomedicine, economics, sociology, educational psychology. Semiparametric monotonic transformation models not only can be used in a wide range of application and not be easy to cause the misjudgment of model, but also are similar to the linear model of explanatory. This project is going to research on the following three problems: maximum rank correlation estimation and application of mean residual life transformation models with length-biased and right-censored data, semiparametric method and application of monotone hazard transformation models with doubly censoring data, statistical inference and application of generalized partially linear index models with doubly censoring data. By the method of rank estimation, we intend to research the estimations of three kinds of semiparametric monotonic transformation models and their large sample properties. Stochastic simulation and real data analysis will be processed to check the models.

不完全数据广泛存在于生物医学、经济学、社会学、教育心理学等众多领域中。半参数单调转移模型不仅适用范围广、不易引起模型的误判，而且还具有类似于线性模型的易解释性。本项目拟着重研究下面的三个问题：长度偏差右删失数据下均值剩余寿命转移模型的最大秩相关估计及其应用、双边删失数据下单调风险转移模型的半参方法及其应用、双边删失数据下广义部分线性指标模型的统计推断及其应用。我们拟借助秩估计方法，对三类半参数单调转移模型的估计问题及其大样本性质进行研究，且通过随机模拟及实例数据对模型进行检验。

本项目提出合适的光滑目标函数，通过该目标函数估计均值剩余寿命转移模型的回归参数；证明该估计方法满足相合性和渐近正态性。本项目提出单调风险转移模型的回归参数估计方法；探讨该估计的渐近性质。该项目分析其统计理论和方法，对应用进行研究，完善理论证明方法，给出合理、稳定的算法研究，为其它应用性学科提供理论支撑和研究方法。本项目将估计方法应用到胶质瘤患者、企业生存时间、脊髓小脑失调等数据。