若干问题多重比较的研究

发布时间：2018-11-10 08:21

【摘要】：在生物、医学、金融、经济等领域,复杂数据多总体的多重比较问题亟待解决。本文研究了两个多重比较问题:带零对数正态均值的同时置信区间问题及异方差回归模型回归系数的多重检验问题。提供了若干多重比较方法并通过数值模拟比较了不同方法的频率性质。所有方法均可应用到生物、医学等领域的具体数据集。本文首先解决的第一个多重比较问题是多个带零对数正态总体均值的同时置信区间问题。因大多纵向医疗数据均近似服从带零对数正态混合分布,对多个纵向医疗数据集的研究时常需要构造同时置信区间,所以对于带零对数正态均值同时置信区间问题的研究有现实意义且截止目前仍没有相关问题的研究文献。文章第二章探究了基于控制FWER的11种不同的同时置信区间构造法,理论推导了同时置信区间构造过程,提供了相应同时置信区间的蒙特卡罗模拟算法。在处理复杂数据中,多重检验作为分析大量数据的一个主要理论基础是本文研究的第二个多重比较问题。对于k个异方差回归系数的检验是本文感兴趣的。第一步探究k个异方差回归系数相等性的同时检验,在此基础上若原假设被拒绝需继续考虑多重检验问题。本文基于上述过程研究k个异方差回归系数的多重检验并提供了若干种假设检验过程,这些检验均基于控制FDR的BH过程和Step-down过程而完成的。最后针对两个多重比较问题进行数值模拟,数值模拟比较了不同的多重比较方法之间的差异与联系,分析了不同方法在相同参数设定下的优良频率性质,得出结论。
[Abstract]:In biology, medicine, finance, economy and other fields, the multiple comparisons of complex data need to be solved. In this paper, we study two multiple comparison problems: the simultaneous confidence interval problem with zero logarithmic normal mean and the multiple test problem of regression coefficients of heteroscedasticity regression model. Several multiple comparison methods are provided and the frequency properties of different methods are compared by numerical simulation. All methods can be applied to specific data sets in biology, medicine and other fields. In this paper, the first multiple comparison problem is the simultaneous confidence interval problem with zero logarithmic normal population mean. Because most of the longitudinal medical data are similar to the normal distribution with zero logarithm, it is often necessary to construct simultaneous confidence intervals for the study of multiple longitudinal medical data sets. So it is of practical significance to study the simultaneous confidence interval problem with zero logarithmic normal mean and there is no related research literature up to now. In the second chapter, 11 different simultaneous confidence interval construction methods based on control FWER are discussed. The construction process of simultaneous confidence interval is derived theoretically, and the Monte Carlo simulation algorithm of corresponding simultaneous confidence interval is provided. In dealing with complex data, as a main theoretical basis for analyzing a large number of data, multiple test is the second multiple comparison problem studied in this paper. The test of k heteroscedasticity regression coefficients is of interest to this paper. The first step is to explore the simultaneous test of k heteroscedastic regression coefficients, and on this basis, if the original hypothesis is rejected, we should continue to consider the multiple test problem. In this paper, we study the multiple tests of k heteroscedasticity regression coefficients based on the above processes and provide several hypothetical test processes, which are based on the BH and Step-down processes that control FDR. Finally, the numerical simulation of two multiple comparison problems is carried out. The difference and relation between different multiple comparison methods are compared by numerical simulation, and the excellent frequency properties of different methods under the same parameters are analyzed, and the conclusion is drawn.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212.1

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