本文選題：同時置信區(qū)間 + 多重比較�。� 參考：《青島大學》2017年碩士論文

【摘要】：在實際問題當中,海量數據具有多個特征,而這些特征參數往往需要同時滿足所需條件,同時置信區(qū)間與多重比較問題就變得越來越重要。本文主要針對生物醫(yī)學統(tǒng)計數據所常見的對數正態(tài)分布和二項分布,對它們的均值進行多重比較以及同時區(qū)間估計的研究,主要結果如下:在第二章,對多個對數正態(tài)分布均值進行兩兩多重比較并構造同時置信區(qū)間。本文首先依據似然比統(tǒng)計量將CAT方法也推廣到兩兩比較中,并構造基于CAT方法的同時似然置信區(qū)間。然后通過Monte-Carlo模擬以及醫(yī)學試驗實例將CAT方法的多重比較和同時似然置信區(qū)間與對應的廣義變量(GV)方法做比較。模擬結果和實例分析顯示多重比較中基于似然比統(tǒng)計量的CAT方法的FWER更接近名義水平,并具有最高的勢;同時置信區(qū)間方面基于CAT方法的同時似然置信區(qū)間長度最短并且最為穩(wěn)健。在第三章,對多個二項分布參數兩兩風險差構造同時置信區(qū)間。針對兩個二項分布總體風險差區(qū)間估計的良好頻率性質,本文首先將兩個二項分布風險差的Fiducial區(qū)間推廣到三個及以上總體兩兩風險差的Fiducial同時置信區(qū)間(FSCI)中,然后根據方差穩(wěn)定變換和Fiducial推斷的方法構造兩兩風險差的廣義同時置信區(qū)間(GSCI),并和已有的Wald方法、Add-1方法、方差估計復原法(MOVER)、Newcombe混合得分(NHS)法同時置信區(qū)間進行比較。數值模擬結果顯示,FSCI、GSCI相對頻率性質更穩(wěn)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.
【學位授予單位】：青島大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.1

【參考文獻】

相關碩士學位論文 前2條

1 徐靜;若干問題多重比較的研究[D];青島大學;2016年

2 易紅玲;多維二項分布參數的同時置信區(qū)間[D];華東師范大學;2010年

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本文編號：1908025