數條迴歸直線之多重比較

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李晧成(Hao-Cheng Lee) 查詢紙本館藏

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統計研究所

論文名稱

數條迴歸直線之多重比較
(Multiple Comparison of Several Regression Lines)

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摘要(中)

本文針對具有常態分布誤差的數個迴歸模式，於其共變數可能範圍內，建立多條迴歸直線與一條對照迴歸直線差異之聯合單尾信賴域。針對具有單一共變數的兩條迴歸直線差異，本文求出確實的雙尾信賴帶或單尾信賴域之後應用Bonferroni不等式調整族誤差率以建立相關的聯合雙尾信賴帶或聯合單尾信賴域。針對具有多個共變數的數條迴歸直線比較，則是利用模擬的方法求得建立此一聯合單尾信賴域所需之臨界值。本文並進一步利用模擬方法，研究所提聯合單尾信賴域的覆蓋機率。最後，以實例說明所提方法之應用。

摘要(英)

The problem of interest in this article is to construct simultaneous one-sided confidence regions for the difference between one controlled regression line with other several regression lines when the random errors are normally distributed. We propose an exact two-sided confidence band or one-sided confidence region for the difference of two simple linear regression lines and then suggest to construct such a simultaneous two-sided confidence band or one-sided confidence region by applying Bonferroni’s inequality for controlling the experiment error rate. For the comparison of several regression lines with one regression line when two or more covariates are involved, we consider to use a simulation-based method for finding the required critical value in the simultaneous one-sided confidence region. A simulation study is then conducted to investigate the coverage probability of the proposed confidence region. Finally, the application of the proposed procedures are demonstrated by illustrating a real data set.

關鍵字(中)

★ 迴歸直線
★ 多重比較
★ 聯合雙尾信賴帶
★ 聯合單尾信賴域

關鍵字(英)

★ regression line
★ simultaneous one-sided confidence regions
★ multiple comparison
★ simultaneous two-sided confidence band

論文目次

第一章研究動機及目的……………………………… 1
第二章文獻回顧……………………………………… 3
2.1單一共變數之下平均反應的單尾聯合信賴域…… 3
2.2 數條迴歸直線的多重比較………………………… 7
第三章統計方法……………………………………… 11
3.1具單一共變數數條迴歸直線之多重比較………… 11
3.2具多個共變數數條迴歸直線之多重比較………… 14
3.3 封閉性多重比較 ……………………………………18
第四章模擬研究……………………………………… 19
第五章實例分析……………………………………… 22
第六章結論及未來研究……………………………… 25
參考文獻 ……………………………………………… 26
附錄一定理證明……………………………………… 44
附錄二實例原始資料………………………………… 51

參考文獻

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指導教授

陳玉英(Yuh-Ing Chen)

審核日期

2007-7-17

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