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    Title: 移動平均式的卡方檢定與其他無母數檢定法的比較
    Other Titles: A study of power performance of the average shifted Chi-square test for goodness of fit
    Authors: 黃貞維;Huang, Chen-wei
    Contributors: 淡江大學統計學系碩士班
    鄧文舜
    Keywords: 卡方檢定;適合度檢定;移動平均式的卡方檢定;Chi-square test;Goodness of fit test;Average shifted chi-square test
    Date: 2010
    Issue Date: 2010-09-23 16:42:05 (UTC+8)
    Abstract: 當給定一組隨機觀測值 ,如欲檢定它們是否來自某特定連續型母體分布,稱為適合度檢定(goodness of fit test ),其中卡方檢定(Pearson chi-square test) 為常見的方法。使用卡方檢定時須先給定樣本空間的分組數(number of partition),再計算每個組別中的期望次數和理論次數的差異,作為卡方檢定統計量,因檢定統計量會受到起始點選擇的影響,造成統計量不穩定。此外,樣本空間的分組,使得樣本資訊損失造成檢定力下降的問題,由於上述兩缺點,Wu and Deng (2010) 提出移動平均式卡方檢定,將單一起始點的卡方檢定推廣到多個起始點,減少起始點對檢定統計量的影響。
    本文使用三個準則檢視移動平均式卡方的穩定度,發現起始點個數增加時移動平均式卡方統計量越趨於穩定,當起始點個數大於5後,穩定度的改善趨於平緩。此外本文將移動平均式卡方檢定和其他適合度檢定( Kolmogorov-Smirnov檢定、Anderson-Darling檢定、Cramér-Von Mises檢定) 進行模擬比較。
    Given a random sample of size n, consider the problem of testing the null hypothesis that the sample has been drawn from a continuous distribution will be goodness of fit test. Pearson chi-squared test is the popular of goodness of fit test. Use Pearson chi-squared test should be decision number of partition. Calculated the difference number between the expectations and theory of each group. So the value of test statistics depends on the choice of these intervals’ anchor position. Wu and Deng (2010) propose average shifted chi-square test to less sensitive to the choice of anchor point.

    In this paper we used three criteria to view the stability of test statistics. When the starting point increases, then the average shifted chi-square statistics tend toward stability. The study also to compare the average shifted chi-square test and other goodness of fit test.
    Appears in Collections:[Graduate Institute & Department of Statistics] Thesis

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