左截断右删失数据下剩余寿命分位数的置信区间构造

发布时间：2018-02-22 15:47

本文关键词： 左截断右删失剩余寿命分位数置信区间 Bootstrap-t Jackknife-d　出处：《兰州财经大学》2017年硕士论文　论文类型：学位论文

【摘要】：在医学的临床研究中,数据往往同时存在删失和截断。近年来删失和截断数据在剩余寿命分位数的研究中已经变得越来越普遍。本文主要针对左截断右删失数据讨论了剩余寿命分位数的置信区间构造问题。在截断和删失数据下或样本量很小时,传统的置信区间构造方法通常是不理想的,而且涉及到参数估计的渐近方差计算相当繁琐。本文从重抽样的角度出发,构造剩余寿命函数分位数的置信区间。Jackknife-d方法是实际中最常用的一种重抽样方法,与传统的置信区间构造方法相比,可以充分地利用感兴趣变量之外的辅助信息。同时,在非平滑函数下得到的方差估计也具有无偏性等优点。另一方面,Bootstrap-t方法可以直接从数据中获得的信息来构造置信区间,不包括任何理论假设,并且在小样本情况下也表现出较好的覆盖误差。因此,本文分别利用Jackknife-d方法和Bootstrap-t方法构造了左截断右删失数据下剩余寿命函数分位数的置信区间并分别给出了估计量相应的渐近性质。同时,通过Monte Carlo模拟和实例分析对两种重抽样方法和传统的四种方法进行评价。模拟结果表明:小样本情况下,本文提出的两种重抽样方法在区间长度较传统方法有明显的优势。其中,Jackknife-d方法构造的区间区间长度最短,是小样本下一种理想的区间构造方法。
[Abstract]:In the clinical research of medicine, In recent years, censored and truncated data have become more and more common in the study of residual life quantiles. In this paper, the residual life quantiles are mainly discussed for left truncated and right censored data. With truncated and censored data or small sample sizes, The traditional method of constructing confidence interval is usually not ideal, and the calculation of asymptotic variance involving parameter estimation is rather complicated. The Jackknife-d method for constructing the quantile of residual life function is one of the most commonly used resampling methods in practice. Compared with the traditional confidence interval construction method, it can make full use of the auxiliary information other than the variables of interest. On the other hand, the Bootstrap-t method can construct confidence intervals directly from the information obtained from the data, and does not include any theoretical assumptions. And it also shows good coverage error in the case of small sample. In this paper, Jackknife-d method and Bootstrap-t method are used to construct the confidence interval of the quantile of the residual life function under the left truncation and the right censored data, and the asymptotic properties of the estimator are given respectively. Two resampling methods and four traditional methods are evaluated by Monte Carlo simulation and case analysis. The simulation results show that: in the case of small sample, The two resampling methods proposed in this paper have obvious advantages over the traditional method in interval length. Jackknife-d method is the shortest interval length and is an ideal interval construction method for small samples.
【学位授予单位】：兰州财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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