双删失数据下共享脆弱性模型半参数有效估计

发布时间：2018-01-05 22:12

本文关键词：双删失数据下共享脆弱性模型半参数有效估计　出处：《中国科学技术大学》2017年硕士论文　论文类型：学位论文

【摘要】：在这篇文章中,我们针对左右删失的生存数据,也称双删失数据,研究其生成的脆弱性模型。这个模型对当前生存模型的领域有一定的延伸,具体来说,我们把右删失数据在脆弱性模型当中的应用扩充到具有额外左删失数据的更复杂的情况。在这个模型中,我们采用似然函数方法来估计未知参数,在估参过程中采用核心算法是EM算法。基于我们建立的模型特殊性——其中含有无限维参数,在研究中借助非参数最大似然估计法(NPMLE)估计无限维参数;此外对于其他参数,由于没有显式形式,估计会运用到牛顿迭代法。在估参的过程中会涉及到计算量过大的问题,所以我们会对EM算法进行改善,采用MCEM算法来降低计算量。在有限维参数中,运用半参数最大似然方法后要建立相应的渐近特性。之后文章后面会讨论运用自助法估计的标准差相容性问题。于此同时,我们查找一些数据拟合到建立的模型中运用新算法评价其估计量和稳健性。
[Abstract]:In this paper, we study the generated vulnerability model for the left and right censored survival data, also known as double-censored data. This model has a certain extension of the current survival model domain, specifically. We extend the application of right censored data in the vulnerability model to more complex cases with additional left censored data. In this model, we use the likelihood function method to estimate unknown parameters. In the process of parameter estimation, the core algorithm is EM algorithm, based on the particularity of our model, which contains infinite dimensional parameters. In this study, the nonparametric maximum likelihood estimation (NPMLEA) is used to estimate the infinite dimensional parameters. In addition, for other parameters, because there is no explicit form, the estimation will be applied to Newton iteration method. In the process of estimating parameters, the calculation will be too large, so we will improve the EM algorithm. The MCEM algorithm is used to reduce the computation cost in finite dimensional parameters. The asymptotic properties of the semi-parametric maximum likelihood method should be established. The compatibility of the standard deviation estimated by the self-help method will be discussed later in this paper. At the same time. We find some data fitting to the established model and use the new algorithm to evaluate its estimator and robustness.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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