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中文論文名稱 頻率移動平均卡方統計量
英文論文名稱 Moving Average Frequency Chi-square Statistics
校院名稱 淡江大學
系所名稱(中) 中等學校教師在職進修數學教學碩士學位班
系所名稱(英) Executive Master's Program In Mathematics for Teachers
學年度 101
學期 2
出版年 102
研究生中文姓名 蕭任嫻
研究生英文姓名 Jen-Hsien Hsiao
學號 700190084
學位類別 碩士
語文別 中文
口試日期 2013-06-29
論文頁數 31頁
口試委員 指導教授-伍志祥
委員-張三奇
委員-楊恭漢
中文關鍵字 頻率移動平均卡方統計量  適合度檢定 
英文關鍵字 moving average frequency chi-square statistics  goodness-of-fit test  overlapping cells 
學科別分類
中文摘要 給定一組連續型分布的隨機樣本,傳統的卡方適合度檢定會因分組起始點選取的不同,導致不同的檢定結果,Wu 和Deng(2010)提出移動平均卡方檢定統計量,來改善個問題。在模擬研究時,發現在對立假設的某一分布下,相鄰樣本數的檢定力會產生不小差異,這表示卡方適合度檢定對樣本數敏感。
本論文提出頻率移動平均卡方統計量(moving average frequency chi-square statis- tics),是一般化Wu 和Deng(2010)的方法。首先,將[0,1]切割成m個區間,並計算每一區間擁有的樣本頻率,再取相鄰的l個區間的樣本頻率值,計算l階頻率移動平均值,再以此l階移動平均值為基礎,建立卡方統計量,並稱此為頻率移動平均卡方統計量(MAFCS)。我們可以藉由U統計量的理論,證明MAFCS的漸進分布會趨近於有限個自由度1的卡方變數的線性組合。利用模擬數據分析可知,MAFCS可改善檢定力對樣本數的敏感,另外對於震盪頻率較高的分布函數,MAFCS可提供比尼曼平滑檢定與Anderson Darling檢定更高的檢定力。
英文摘要 Given a set of observations from a continuous distribution, consider the problem of testing whether the sample has been drawn from a population with a specified probability density based on grouping of data. The chi-square test would be very sensitive to the choice of anchor (cell origin) and lead to different test results of power, between adjacent sample sizes, such not as a reference to each other. Therefore, in this presentation, it is the idea of moving average frequency that gives rise to generalize the averaged of shifted chi-squared test, proposed by Wu and Deng(2010). Computing moving average frequency values and use these values to construct chi-square statistics. Call the proposed test statistics moving average frequency chi-square statistics (MAFCS). By the theory of U-statistics, we prove that the proposed MAFCS is asymptotically distributed as a finite linear combination of chi-square variables of degree 1. The simulated power comparisons show that, MAFCS can improve the pro- blem of reference the results between adjacent sample sizes and lead to better gains than Neyman Smooth tests and Anderson-Darling tests in power.
論文目次 第1節 緒論………………………………………….....1
第2節 頻率移動式卡方檢定量的介紹……………….3
第3節 數值模擬分析………………………………….8
3.1 檢定力之改善…………………………………8
3.2 檢定力之比較…………………………………9
第4節 建議……………………………………………16
參考文獻………………………………………………..17
附錄……………………………………………………..18
參考文獻 A. J. Viollaz (1986). On the Reliability of the Chi-square Test. Metrica, 33, 135-142.
A. J. Lee(1990). U-statistics: Theory and Pracyice, New York: Marcel-Dekker, pp.
79-83.
G. D. Rayner,& J. C. W. Rayner (2001). Power of the Neyman Smooth Tests for the
Uniform Distribution. Journal of Applied Mathmatics and Decision Sciences, 5(3),
181-191.
J. S. Wu,& W. S. Deng (2010). Averaged shifted chi-square test. Journal of Nonpa-
rametric Statistics, 1(24), 39-57.
J. C. W. Rayner,& D. J. Best(2000). Goodness of fit: methods and models. To appear
in the International Encyclopaedia of Social and Behavioral Sciences.
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