發(fā)布時(shí)間：2018-11-10 08:21

【摘要】：在生物、醫(yī)學(xué)、金融、經(jīng)濟(jì)等領(lǐng)域,復(fù)雜數(shù)據(jù)多總體的多重比較問題亟待解決。本文研究了兩個(gè)多重比較問題:帶零對(duì)數(shù)正態(tài)均值的同時(shí)置信區(qū)間問題及異方差回歸模型回歸系數(shù)的多重檢驗(yàn)問題。提供了若干多重比較方法并通過數(shù)值模擬比較了不同方法的頻率性質(zhì)。所有方法均可應(yīng)用到生物、醫(yī)學(xué)等領(lǐng)域的具體數(shù)據(jù)集。本文首先解決的第一個(gè)多重比較問題是多個(gè)帶零對(duì)數(shù)正態(tài)總體均值的同時(shí)置信區(qū)間問題。因大多縱向醫(yī)療數(shù)據(jù)均近似服從帶零對(duì)數(shù)正態(tài)混合分布,對(duì)多個(gè)縱向醫(yī)療數(shù)據(jù)集的研究時(shí)常需要構(gòu)造同時(shí)置信區(qū)間,所以對(duì)于帶零對(duì)數(shù)正態(tài)均值同時(shí)置信區(qū)間問題的研究有現(xiàn)實(shí)意義且截止目前仍沒有相關(guān)問題的研究文獻(xiàn)。文章第二章探究了基于控制FWER的11種不同的同時(shí)置信區(qū)間構(gòu)造法,理論推導(dǎo)了同時(shí)置信區(qū)間構(gòu)造過程,提供了相應(yīng)同時(shí)置信區(qū)間的蒙特卡羅模擬算法。在處理復(fù)雜數(shù)據(jù)中,多重檢驗(yàn)作為分析大量數(shù)據(jù)的一個(gè)主要理論基礎(chǔ)是本文研究的第二個(gè)多重比較問題。對(duì)于k個(gè)異方差回歸系數(shù)的檢驗(yàn)是本文感興趣的。第一步探究k個(gè)異方差回歸系數(shù)相等性的同時(shí)檢驗(yàn),在此基礎(chǔ)上若原假設(shè)被拒絕需繼續(xù)考慮多重檢驗(yàn)問題。本文基于上述過程研究k個(gè)異方差回歸系數(shù)的多重檢驗(yàn)并提供了若干種假設(shè)檢驗(yàn)過程,這些檢驗(yàn)均基于控制FDR的BH過程和Step-down過程而完成的。最后針對(duì)兩個(gè)多重比較問題進(jìn)行數(shù)值模擬,數(shù)值模擬比較了不同的多重比較方法之間的差異與聯(lián)系,分析了不同方法在相同參數(shù)設(shè)定下的優(yōu)良頻率性質(zhì),得出結(jié)論。
[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.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O212.1

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本文編號(hào)：2321914