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題名 以逐次方法縮減估計值變異數的模擬研究
Variance Reduction: A Simulation Study of Sequential Methods
作者 吳振興
Wu, Chen-Hsing
貢獻者 余清祥
Jack Yue, Ching-Syang
吳振興
Wu, Chen-Hsing
關鍵詞 逐次
期望值
模擬
Sequential
Expectation
Simulation
日期 1999
上傳時間 30-Mar-2016 19:08:04 (UTC+8)
摘要 在本文中使用七種不同的抽樣方法估計對稱分配的位置參數，目的是為了縮減估計值的變異數。我們考慮的方法是四種逐次估計量、Trimmed Mean、修正隨機估計量和加權隨機估計量。本文利用電腦模擬的方式，比較在觀察值為標準常態分配之下這幾種估計量與簡單隨機抽樣的樣本平均數估計值的變異數大小。
In this paper seven sampling methods are used to estimate the mean of symmetric distributions. Our goal is reduce the variance of the estimate. The methods we consider include four sequential estimators, trimmed mean, adjusted random estimator, and weighted random estimator. This paper uses the method of computer simulation to compare variance of these estimators with sample mean using simple random sampling method under standard normal distribution.
參考文獻 [1] Caperaa, P. and Rivest, L.P.(1995), On the variance of the trimmed mean, Statistics & Probability Letters, 22, 79-85.
     [2] David, H.A and Balakrishna, N.(1996), Product moments of order statistics and the variance of a lightly trimmed mean, Statistics & Probability Letters, 29, 85-87.
     [3] Mehrotra, K. and Jackson, P.(1991), On choosing an optimally trimmed mean, Communications in Statistics, Part B—Simulation and Computation, 20(1), 73-80.
     [4] Oosterhoff, J.(1994), Trimmed mean or sample median ?, Statistics & Probability Letters, 20, 401-409.
     [5] Shorack, G.R.(1974), Random means, The Annals of Statistics, Vol.2, No.4, 661-675.
     [6] Stigler, S.M.(1973), The asymptotic distribution of the trimmed mean, The Annals of Statistics, Vol.1, No.3, 472-477.
     [7] Stigler, S.M.(1974), Linear functions of order statistics with smooth weight functions, The Annals of Statistics, Vol.2, No.4, 676-693.
描述 碩士
國立政治大學
統計學系
86354020
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001930
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.advisor Jack Yue, Ching-Syangen_US
dc.contributor.author (Authors) 吳振興zh_TW
dc.contributor.author (Authors) Wu, Chen-Hsingen_US
dc.creator (作者) 吳振興zh_TW
dc.creator (作者) Wu, Chen-Hsingen_US
dc.date (日期) 1999en_US
dc.date.accessioned 30-Mar-2016 19:08:04 (UTC+8)-
dc.date.available 30-Mar-2016 19:08:04 (UTC+8)-
dc.date.issued (上傳時間) 30-Mar-2016 19:08:04 (UTC+8)-
dc.identifier (Other Identifiers) A2002001930en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83108-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 86354020zh_TW
dc.description.abstract (摘要) 在本文中使用七種不同的抽樣方法估計對稱分配的位置參數，目的是為了縮減估計值的變異數。我們考慮的方法是四種逐次估計量、Trimmed Mean、修正隨機估計量和加權隨機估計量。本文利用電腦模擬的方式，比較在觀察值為標準常態分配之下這幾種估計量與簡單隨機抽樣的樣本平均數估計值的變異數大小。zh_TW
dc.description.abstract (摘要) In this paper seven sampling methods are used to estimate the mean of symmetric distributions. Our goal is reduce the variance of the estimate. The methods we consider include four sequential estimators, trimmed mean, adjusted random estimator, and weighted random estimator. This paper uses the method of computer simulation to compare variance of these estimators with sample mean using simple random sampling method under standard normal distribution.en_US
dc.description.tableofcontents 封面頁
     證明書
     致謝詞
     論文摘要
     目錄
     圖目錄
     第一章 導論
     1.1 研究動機與目的
     1.2 研究方法
     1.3 文獻回顧
     1.4 本文架構
     第二章 模擬
     2.1 Fixed Estimator
     2.2 Partial-Sequence Estimator
     2.3 Sequential Estimator
     2.4 Trimmed Mean
     2.5 其他抽樣方法
     2.5.1 Adjusted Fixed Estimator
     2.5.2 Other Random Estimator
     2.5.2.1 Adjusted Random Estimator
     2.5.2.2 Weighted Random Estimator
     第三章 證明
     3.1 Fixed Estimator 的不偏性
     3.2 Partial-Sequence Estimator的不偏性
     3.3 Sequential Estimator 的不偏性
     3.4 變異數的比較
     第四章 結論與未來研究方向
     4.1 結論
     4.2 未來研究方向
     附錄
     附錄一：模擬程式
     程式一：Fixed Estimator的模擬
     程式二：Fixed Estimator和簡單隨機抽樣的樣本平均數(樣本數為n+m)的模擬
     程式三：Fixed Estimator、Partial-Sequence Estimator和簡單隨機抽樣的樣本平均數(樣本數為n+m)的模擬
     程式四：Fixed Estimator、Sequential Estimator和簡單隨機抽樣的樣本平均數(樣本數為n+m)的模擬
     程式五：Trimmed Mean和簡單隨機抽樣的樣本平均數(樣本數為n)的模擬
     程式六：期望值的模擬(詳見58頁)
     程式七：Adjusted Fixed Estimator、Fixed Estimator和簡單隨機抽樣的樣本平均數(樣本數為n+m)的模擬
     程式八：Random Estimator、Adjusted Random Estimator與Weighted Random Estimator變異數的模擬
     附錄二：模擬結果的數值部分
     表2-1　在 n + m = 200 下 Fixed Estimator 變異數的模擬
     表2-2　在 n + m = 500 下 Fixed Estimator 與 Xn+m變異數的模擬
     表2-3　在 n = 50 下 Fixed Estimator、Partial-Sequence Estimator 與 Xn+m 變異數的模擬
     表2-4　Fixed Estimator、Partial-Sequence Estimator 與 Xn+m 變異數的模擬
     表2-5　Fixed Estimator、Sequential Estimator 與 Xn+m 變異數的模擬
     表2-6　Trimmed Mean 與 Xn+m 變異數的模擬
     表2-7　在 n + m = 500, C=2 和 3 下 Fixed Estimator、Adjusted Fixed Estimator 與 Xn+m變異數的模擬
     表2-8　Random Estimator、Adjusted Random Estimator 與 Weighted Random Estimator 變異數的模擬
     表2-9　在相同有效樣本數下 Fixed Estimator 和 Trimmed Mean 的模擬
     表2-10　在相同有效樣本數下 Partial-Sequence Estimator 和 Trimmed Mean 的模擬
     表2-11　在相同有效樣本數下 Sequential Estimator 和 Trimmed Mean 的模擬
     表2-12　Fixed Estimator 與 Xn+1變異數的比較
     附錄三：參考文獻		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001930en_US
dc.subject (關鍵詞) 逐次zh_TW
dc.subject (關鍵詞) 期望值zh_TW
dc.subject (關鍵詞) 模擬zh_TW
dc.subject (關鍵詞) Sequentialen_US
dc.subject (關鍵詞) Expectationen_US
dc.subject (關鍵詞) Simulationen_US
dc.title (題名) 以逐次方法縮減估計值變異數的模擬研究zh_TW
dc.title (題名) Variance Reduction: A Simulation Study of Sequential Methodsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Caperaa, P. and Rivest, L.P.(1995), On the variance of the trimmed mean, Statistics & Probability Letters, 22, 79-85.
     [2] David, H.A and Balakrishna, N.(1996), Product moments of order statistics and the variance of a lightly trimmed mean, Statistics & Probability Letters, 29, 85-87.
     [3] Mehrotra, K. and Jackson, P.(1991), On choosing an optimally trimmed mean, Communications in Statistics, Part B—Simulation and Computation, 20(1), 73-80.
     [4] Oosterhoff, J.(1994), Trimmed mean or sample median ?, Statistics & Probability Letters, 20, 401-409.
     [5] Shorack, G.R.(1974), Random means, The Annals of Statistics, Vol.2, No.4, 661-675.
     [6] Stigler, S.M.(1973), The asymptotic distribution of the trimmed mean, The Annals of Statistics, Vol.1, No.3, 472-477.
     [7] Stigler, S.M.(1974), Linear functions of order statistics with smooth weight functions, The Annals of Statistics, Vol.2, No.4, 676-693.		zh_TW