多总体比较的同时置信区间

发布时间：2018-05-19 01:08

本文选题：同时置信区间 + 多重比较　；参考：《青岛大学》2017年硕士论文

【摘要】：在实际问题当中,海量数据具有多个特征,而这些特征参数往往需要同时满足所需条件,同时置信区间与多重比较问题就变得越来越重要。本文主要针对生物医学统计数据所常见的对数正态分布和二项分布,对它们的均值进行多重比较以及同时区间估计的研究,主要结果如下:在第二章,对多个对数正态分布均值进行两两多重比较并构造同时置信区间。本文首先依据似然比统计量将CAT方法也推广到两两比较中,并构造基于CAT方法的同时似然置信区间。然后通过Monte-Carlo模拟以及医学试验实例将CAT方法的多重比较和同时似然置信区间与对应的广义变量(GV)方法做比较。模拟结果和实例分析显示多重比较中基于似然比统计量的CAT方法的FWER更接近名义水平,并具有最高的势;同时置信区间方面基于CAT方法的同时似然置信区间长度最短并且最为稳健。在第三章,对多个二项分布参数两两风险差构造同时置信区间。针对两个二项分布总体风险差区间估计的良好频率性质,本文首先将两个二项分布风险差的Fiducial区间推广到三个及以上总体两两风险差的Fiducial同时置信区间(FSCI)中,然后根据方差稳定变换和Fiducial推断的方法构造两两风险差的广义同时置信区间(GSCI),并和已有的Wald方法、Add-1方法、方差估计复原法(MOVER)、Newcombe混合得分(NHS)法同时置信区间进行比较。数值模拟结果显示,FSCI、GSCI相对频率性质更稳健。
[Abstract]:Among practical problems, mass data has many features, and these feature parameters often need to meet the required conditions simultaneously. Meanwhile, confidence intervals and multiple comparisons become more and more important. In this paper, the logarithmic normal distribution and binomial distribution, which are common in biomedical statistics, are studied in terms of multiple comparisons of their mean values and simultaneous interval estimation. The main results are as follows: in Chapter 2, The multiple lognormal distribution means are compared and the simultaneous confidence intervals are constructed. In this paper, the CAT method is extended to pairwise comparison based on likelihood ratio statistics, and the simultaneous likelihood confidence interval based on CAT method is constructed. Then the multiple comparisons and simultaneous likelihood confidence intervals of the CAT method are compared with the corresponding generalized variables by Monte-Carlo simulation and medical experiments. Simulation results and case studies show that the FWER of CAT method based on likelihood statistics is closer to the nominal level and has the highest potential. The simultaneous likelihood confidence interval based on CAT method is the shortest and most robust. In chapter 3, we construct simultaneous confidence intervals for multiple binomial distribution parameters. In view of the good frequency properties of the interval estimation of the risk difference between two binomial distributions, this paper first extends the Fiducial interval of the two binomial distribution risk difference to the Fiducial simultaneous confidence interval of three or more binomial risk differences. Then the generalized simultaneous confidence interval (GCS) of the pairwise risk difference is constructed according to the variance stability transformation and the Fiducial inference method, and the confidence interval is compared with the existing Wald method / Add-1 method and the variance estimation restoration method / Fiducial method. The numerical simulation results show that the relative frequency properties of FSCI GSCI are more robust.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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