收缩估计和惩罚估计在Gamma删失回归模型中的应用

发布时间：2018-06-28 13:25

本文选题：Gamma删失回归模型 + 收缩估计　；参考：《兰州大学》2016年硕士论文

【摘要】：本文考虑了在生存分析领域有着广泛应用的Gamma删失回归模型(因变量服从Gamma分布的删失回归模型)的参数估计问题.我们的目的是在预测变量中可能存在一些与因变量不相关的情况下,运用Stein类型的收缩估计来改善传统的估计方法.在Gamma删失回归模型中我们给出了两种模型:考虑全部变量的全模型(full model)和利用先验信息剔除不相关变量之后的子模型(candidate model).在均方误差的意义下,结合全模型和子模型的收缩估计的估计效果要优于单独考虑全模型或子模型的估计效果.我们同时考虑了Lasso,Adaptive Lasso,SCAD三种惩罚估计,比较了收缩估计和惩罚估计的估计效果.我们同时还进行了大量的模拟研究,结果表明:收缩估计的估计效果要优于惩罚估计.我们还进行了实证分析,将收缩估计和惩罚估计应用在口咽癌数据和糖尿病数据中,证明了这种方法具有良好的应用前景.
[Abstract]:In this paper, we consider the parameter estimation of Gamma censored regression model, which is widely used in the field of survival analysis. Our aim is to improve the traditional estimation method by using Stein type contraction estimation in the case that there may be some independent variables in the prediction variables. In the Gamma censored regression model, we give two models: the whole model (full model) which considers all variables and the submodel (candidate model). Which uses prior information to remove irrelevant variables. In the sense of mean square error, the estimation effect of the whole model and the submodel is better than that of the whole model or the submodel. At the same time, we consider three kinds of penalty estimators of Lassov Adaptive Lassop SCAD, and compare the estimation effect of contraction estimation and penalty estimation. At the same time, a large number of simulation studies have been carried out. The results show that the estimation effect of the contraction estimation is better than that of the penalty estimation. We also applied the contraction estimation and penalty estimation to the data of oropharynx cancer and diabetes mellitus, which proved that this method has a good application prospect.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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