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。

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

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.