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研究生:陳玟君
研究生(外文):Wen-chun Chen
論文名稱:迴歸係數與係數比值之廣義聯合信賴區域
論文名稱(外文):Generalized Simultaneous Confidence Region for Regression Coefficients and Their Ratio
指導教授:林彩玉林彩玉引用關係
指導教授(外文):Tsai-yu Lin
學位類別:碩士
校院名稱:逢甲大學
系所名稱:應用數學所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:48
中文關鍵詞:Bonferroni 校正廣義變數廣義樞紐量多變量t 分配優勢比覆輔v廣義信賴區間
外文關鍵詞:Generalized pivotal quantityDominance ratioCoverage rateBonferroni correctionGeneralized confidence intervalGeneralized variable approachMultivariate-t distribution
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在動植物的育種試驗中,培育者所感興趣的是顯性(dominance)與累加
(additive)效應的比值,稱之為優勢比(dominance ratio)。因此,如何在線性模型中,
找出兩迴歸係數與其比值的聯合信賴區域(simultaneous confidence region)是值得
探討的問題。過去文獻對於此聯合信賴區域所建議的估計方法是架構在多變量t
分配(multivariate-t distribution)之下的Worst-case與Plug-in (I)兩種方法。本研究則
利用廣義樞紐量(Generalized Pivotal Quantities)的概念提出三種估計方法,分別為
Plug-in (II)、Bonferroni 修正法與廣義變數法(Generalized Variable approach)。接
著,我們透過模擬分析計算此五種方法的聯合信賴區域,再針對各種方法所求得
之覆?#63841;(coverage rate)評估其成效。最後,藉由分析結果整理出一些結論與建
議,並輔以實例說明如何建構本研究所提供聯合信賴區域之程序。
Breeders are usually interested in inferences on the ratio along with the
dominance and additive effects. This thesis considers the problem of finding
simultaneous confidence region for two regression coefficients and their ratio of
general linear models. We use the concept of generalized pivotal quantities to
construct the simultaneous confidence region including Plug-in (II), Bonferroni
correction and Generalized Variable approach. The proposed methods are compared
with the two traditional methods, Worst-case and Plug-in (I), based on the
multivariate-t distribution. A simulation study using the dominance ratio in crossing
experiments with plants is computed from an estimate of the dominance and additive
gene effects. Detailed statistical simulation studies are conducted to evaluate their
performance by the coverage rate. Furthermore, some practical examples are given to
illustrate the proposed procedures.
目錄
誌謝................................................................................................................................i
中文摘要........................................................................................................................ii
英文摘要.......................................................................................................................iii
目錄...............................................................................................................................iv
圖目錄...........................................................................................................................vi
表目錄..........................................................................................................................vii
第一章 緒論..................................................................................................................1
1.1 研究動機與背景................................................................................................1
1.2 研究目的............................................................................................................2
1.3 研究架構............................................................................................................3
第二章 相關研究探討..................................................................................................4
2.1 聯合信賴區域之模型架構.................................................................................4
2.2 廣義信賴區間.....................................................................................................5
第三章 研究方法..........................................................................................................7
3.1 多變量 t 分配程序..............................................................................................7
3.1.1 Worst-case..................................................................................................8
3.1.2 Plug-in (I) ..................................................................................................9
3.1.3 Plug-in (II)..................................................................................................9
3.2 廣義樞紐量法...................................................................................................11
3.2.1 Bonferroni 修正法....................................................................................11
3.2.2 廣義變數法..............................................................................................12
第四章 研究分析與結果............................................................................................14
4.1 模擬之參數設定..............................................................................................14
4.2 覆輔v之結果分析..........................................................................................18
第五章 實例分析........................................................................................................36
5.1 實例一 (新藥開發成效).................................................................................36
5.2 實例二 (基因效應的影響) ............................................................................39
5.3 實例三 (新生兒平均體重) ............................................................................42
第六章 結論................................................................................................................45
參考文獻......................................................................................................................46
圖目 錄
圖 4.1 Worst-case、Plug-in(I)與Plug-in (II)覆輔v之程式流程圖......................16
圖4.2 Bonferroni 修正法與GV 法覆輔v之程式流程圖.................................17
圖5.1 實例一利用五種估計方法所求聯合信賴區域之圖形............................38
圖5.2 實例二利用五種估計方法所求聯合信賴區域之圖形............................41
圖5.3 實例三利用五種估計方法所求聯合信賴區域之圖形............................44
表目 錄
表 4.1 三種基因型態所對應之Z 與W 值............................................................15
表4.2 不同程度的優勢比? ?? ? (? ?j 0 ).........................................................15
表4.3 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數為10) .............................................................................................20
表4.4 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................20
表4.5 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................21
表4.6 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................21
表4.7 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數10) .................................................................................................22
表4.8 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................22
表4.9 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................23
表4.10 五種估計方法模擬5000 次後之覆輔v( 3 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................23
表4.11 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數10) .................................................................................................24
表4.12 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................24
表4.13 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................25
表4.14 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................25
表4.15 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數10) .................................................................................................26
表4.16 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................26
表4.17 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................27
表4.18 五種估計方法模擬5000 次後之覆輔v( 2 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................27
表4.19 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數10) .................................................................................................28
表4.20 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................28
表4.21 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................29
表4.22 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................29
表4.23 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數10) .................................................................................................30
表4.24 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................30
表4.25 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................31
表4.26 五種估計方法模擬5000 次後之覆輔v( 1 1 ? ? ?{ , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................31
表4.27 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數10) .................................................................................................32
表4.28 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數20) .................................................................................................32
表4.29 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數50) .................................................................................................33
表4.30 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? , 任兩基因型之
樣本數100) ...............................................................................................33
表4.31 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? ?{ , 任兩基因型
之樣本數10) .............................................................................................34
表4.32 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? ?{ , 任兩基因型
之樣本數20) .............................................................................................34
表4.33 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? ?{ , 任兩基因型
之樣本數50) .............................................................................................35
表4.34 五種估計方法模擬5000 次後之覆輔v( 0 1 ? ? , 2 2 ? ? ?{ , 任兩基因型
之樣本數100) ...........................................................................................35
表5.1 使用不同藥物之平均肺活量、標準差與人數..........................................36
表5.2 在信賴水準為95%的情況, E P ? ?{? 、R P ? ?{? 與( ) ( ) E P R P ? ?{? ? ?{? 之
估計量、聯合信賴區域與長度..................................................................37
表5.3 不同基因型的胡蘿蔔之平均重量、標準差與個數..................................39
表5.4 在信賴水準為95%的情況,累加效應? 、顯性效應? 與優勢比? ?? ?
之估計量、聯合信賴區域與長度..............................................................40
表5.5 在信賴水準為% 95 的情況下,母親沒抽菸的新生兒平均體重1
? 、母親
有抽菸的新生兒平均體重2 ? 與1 2 ? ? ? ? 之估計量、聯合信賴區域與
長度............................................................................................................43
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