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Student Number 91225018
Author Shih-Chiao Kuo(郭士橋)
Author's Email Address No Public.
Statistics This thesis had been viewed 1666 times. Download 783 times.
Department Graduate Institute of Statistics
Year 2005
Semester 1
Degree Master
Type of Document Master's Thesis
Language zh-TW.Big5 Chinese
Title 有母數強韌迴歸在具相關性資料之樣本數決定問題上之初探
Date of Defense 2005-12-28
Page Count 129
Keyword
  • parametric robust regression
  • sample size
  • Abstract 在處理二變量和三變量的連續資料時,為了分析之便,通常都會假設資料分別服從二維常態和三維常態分配。然而一旦資料不是來自於二維和三維常態分配,則根據二維和三維常態模型所做的推論便是不正確的,而且所決定的樣本將使檢定的型ㄧ誤差機率和檢定力達不到原先的要求。
      本文主要是將 Royall and Tsou (2003)所提出的概似函數修正法應用在二變量和三變量的連續資料平均數的迴歸分析上。說明對二變量和三變量連續資料平均數的迴歸參數而言,二維和三維常態實作模型可以經過適當的修正而被強韌化。在樣本數大的時候,即使資料的真正分配未知,強韌概似函數還是能正確提供相關於有興趣參數的資訊。
      本文也將在簡單線性迴歸模型之下,推導出平均數迴歸參數的概似函數修正項。再利用強韌迴歸方法來決定樣本數,比較在相同的強韌常態模型下,資料服從常態、伽瑪及卡方分配時,所需要樣本數大小之間的差異。
    Table of Content 第 一 章 緒論......................................................1
    第 二 章 強韌迴歸..................................................3
    第 三 章 二維常態模型的修正項......................................5
      3.1  的計算.................................................7
      3.2  的計算................................................17
      3.3 獨立性資料................................................36
      3.4 樣本數的計算..............................................40
    第 四 章 簡單線性迴歸.............................................42
    第 五 章 模擬研究................................................58
      5.1 模擬方法-線性迴歸模型...................................58
      5.2 模擬結果.................................................60
    第 六 章 結論....................................................72
    參考文獻..........................................................73
    附錄A  三維常態模型的修正項.....................................74
      A.1  的計算.................................................77
      A.2  的計算.................................................89
    Reference Hsieh, F.Y., Bloch, D. A. and Larsen, M. D. (1998). A simple method of sample size calculation for liner and logistic regression. Statistics in Medicine, 17, 1623-1634.
    Wolfe, R. and Carlin, J. B. (1999). Sample-size calculation for a log-transformed outcome measure. Controlled Clinical Trials, 20, 547-554.
    Johnson, N. L. and Kotz, S. (1972). Distribution in statistic: Continuous multivariate distributions. John Wiley & Sons, Inc.
    Jensen, D.R. (1970). The joint distribution of quadratic forms and related distributions. Australian Journal of Statistics, 12, 13-22.
    Royall, R. M. and Tsou, T-S (2003). Interpreting statistical evidence using imperfect model: Robust adjusted likelihood functions. J. R. Statist. Soc. B. 65, 391-404.
    Tsou, T-S (2003). Comparing two population means and variances-A parametric robust way. Comm. in Stat. -Theo. and Meth. ,32, 2013-2029.
    Brian Peacock, Merran Evans, Nicholas, Hasting. S.Statistical Distributions Third Edition.Wiley Series in Probability and Statistics.,137-139.
    Tsou, T-S (2004). Parametric robust inferences for regression parameters under generalized linear models. (Submitted)
    許雅嵐 (2004). Parametric robust inference about regression parameters for bivariate
     continuous data. 國立中央大學碩士論文 ,1-48 , 61-67.
    張喬惠 (2004). Determining sample sizes─Parametric robust approaches. 國立中央
     大學碩士論文 , 6-8 , 43-44.
    Advisor
  • Tsung-Shan Tsou(鄒宗山)
  • Files
  • 91225018.pdf
  • approve immediately
    Date of Submission 2006-01-16

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