Nonparametric Linear Model Tests-A Randomization Approach

無母數線性模型的檢定問題運用蒙地卡羅隨機排列法

10.6338/JDA.200912_4(6).0007

李泰明(Tai-Ming Lee)；莊瑞珠(Rwei-Ju Chuang)

多變量線性模式 ； 排列檢定法 ； 蒙地卡羅P值 ； Randomization tests ； Multivariate linear model ； Monte Carlo P-value

Journal of Data Analysis

4卷6期（2009 / 12 / 01）

101 - 115

英文

無母數統計方法運用在兩組獨立樣本和多組獨立樣本上的檢定問題已經有傳統的方法，在統計推論上行之有年。但是若要將這些技術延伸到更複雜的模型上時，都得因模型的不同而有不同的處理方式。這些技術似乎自成一家，尚未能有一個統合的方式將之歸納成一個更一般化的技術，使之運用在線性模型上。本文運用蒙地卡羅隨機排列的技術，將許多的無母數統計方法統合成無母數線性模式。這樣的方式不僅涵蓋範圍廣，更可以將變數轉換成序號再操作，以對抗離群值問題。更重要的是它可以輕易地延伸到多變量反應的模式上，解決了以參數式推論操作多變量線性模式時面臨的複雜數理推演與矩陣運算。許多例題在本文中有完整的操作，如拉丁方格，因子設計，多變量共變異數分析等。

The chief value of Randomization tests lies in their wide range of application. Randomization tests are relatively impervious to complications that defeat other statistical techniques. The major benefit is that they require only one or two relatively weak assumptions. The parametric approaches on Multivariate Linear Model Testing have complicated construction in test statistics, null distributions as well as its asymptotic distributions. In this paper, we develop a simple algorithm, and deeply study how Randomization tests can ease these difficulties. Numerical computation on Monte Carlo P-value and graphical illustration will be demonstrated for both single value response and multivariate response linear model.

1. R. A. Fisher. , “The Design of Experiments”, Edinburgh: Oliver and Boyd, 1935.
2. Edgington, E. S.(1995).Randomization Tests.Marcel Dekker, INC..
3. Good, P.(1994).Permutation Tests. A Practical Guide to Resampling Methods for Testing Hypotheses.Springer-Verlag.
4. Montgomery, D. C.(2001).Design and Analysis of Experiments.John Wiley & Sons, INC..
5. Rencher, A. C.(2002).Methods of Multivariate Analysis.John Wiley:Sons, INC...
6. Weerahandi, S.(1995).Exact Statistical Methods for Data Analysis.Springer-Verlag.