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研究生:鄭雅文
研究生(外文):Cheng, Ya Wen
論文名稱:以無母數方法來檢測變異
論文名稱(外文):A nonparametric test for detecting increasing variability
指導教授:黃子銘黃子銘引用關係
指導教授(外文):Huang, Tzee Ming
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:99
語文別:中文
論文頁數:41
中文關鍵詞:無母數檢定變異
外文關鍵詞:nonparametric testvariability
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當我們探討的是兩組樣本的變異是否有所差異時,常見的方法有以ANOVA 為
基礎的檢定與秩檢定,傳統的秩檢定需要假設兩母體具有相同的中位數或知道
其差異。本研究採用Moses (1963) 提出的rank-like 檢定方法,此方法在處理兩組樣本的變異問題時,優點是不需要估計任何中心參數,也不需要假設母體中心參數相同,在資料偏態的情況下也表現得很穩健,我們試圖在樣本數極小的情況下對此方法作修正,將此檢定方法與以ANOVA 為基礎的檢定和秩檢定進行模擬比較,以能夠良好的控制型一誤差與檢定力作為評斷標準。由模擬的結果可得知,rank-like 檢定方法與修正後的方法在不同的分配下皆表現的穩健而修正後的方法特別適用於小樣本的情形。
We consider the problem of detecting variability change in the two-sample case.Several classical variability tests are investigated, including the ANOVA based tests and the rank tests. Traditional two-sample rank tests assume that the location parameters for both samples are identical or of known difference. In this thesis, a modified version of the distribution-free rank-like test proposed by Moses (1963) is proposed. Moses’s test has several advantages. It does not require location parameter estimation, is applicable without assuming that location parameter are identical, and is robust for skewed data. However, Moses’s test has no power when each of the two samples has size 5 or less. The modified version of Moses’s test proposed in this thesis has some power when the sample sizes are small. Comparative
simulation results are presented. According to these results, both Moses’s test and the proposed test are robust under all conditions, and the proposed test
works better when the sample sizes are small.
1 緒論 7
2 文獻回顧 9
3 研究方法 12
3.1 Moses rank-like 檢定............................. 13
3.2 Moses rank-like 檢定小樣本的改進.................. 14
3.3 Savage 檢定...................................... 15
3.4 Siegel-Tukey 檢定................................ 16
3.5 Conover Squared Rank 檢定........................ 17
3.6 以ANOVA 為基礎的檢定.............................. 17
3.6.1 Brown-Forsythe 檢定........................ 17
3.6.2 O’Brien 檢定.............................. 18
3.6.3 結合Brown-Forsythe 檢定與O’Brien 檢定...... 19
4 模擬分析與討論 20
4.1 模擬設定......................................... 20
4.2 模擬結果與分析.................................... 22
5 結論與建議 37
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