系統識別號 | U0002-0307201321034000 |
---|---|
DOI | 10.6846/TKU.2013.00113 |
論文名稱(中文) | 頻率移動平均卡方統計量 |
論文名稱(英文) | Moving Average Frequency Chi-square Statistics |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 中等學校教師在職進修數學教學碩士學位班 |
系所名稱(英文) | Executive Master's Program In Mathematics for Teachers |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 101 |
學期 | 2 |
出版年 | 102 |
研究生(中文) | 蕭任嫻 |
研究生(英文) | Jen-Hsien Hsiao |
學號 | 700190084 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
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 |
關鍵字(中) |
頻率移動平均卡方統計量 適合度檢定 |
關鍵字(英) |
moving average frequency chi-square statistics goodness-of-fit test overlapping cells |
第三語言關鍵字 | |
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. |
第三語言摘要 | |
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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