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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

J型-發散統計量與數種適合度檢定統計量之比較 / Comparisons of J-divergence statistic with some goodness-of-fit test statistic

吳裕陽, Wu, Yuh Yang Unknown Date (has links)
Taneichi(1993)提出一個新的適合度檢定統計量J<sup>2</sup>,具有近似卡方分配的性質。然而在小樣本的情形下,計算機模擬結果顯示,它的估計顯著水準大於期望顯著水準。所以本論文的重點之一,就是對J<sup>2</sup>進行改進,根據不同的準則,來選取一個適當的常數a。我們建議對每一觀測次數加一常數0.32,作為我們修正後的統計量,這個統計量我們記為J<sub>1</sub><sup>2</sup>。   另一探討的重點是在比較皮爾生卡方統計量X<sup>2</sup>,概似比例統計量G<sup>2</sup>,Cressie & Read統計量 I(2/3),J<sup>2</sup>和J<sub>1</sub><sup>2</sup>之性質,我們想要了解在小樣本的情形之下,何者較接近於卡方分配,何者具有較強的檢定力。研究結果顯示,X<sup>2</sup>和I(2/3)較接近卡方分配,但J<sub>1</sub><sup>2</sup>又較G<sup>2</sup>及J<sup>2</sup>好;至於檢定力,我們發現沒有一個統計量在文中所探討的對立假設的情況下,同時都具有最大的檢定力。這些現象都可以用觀測次數對期望次數比值間的關係來解釋。 / Taneichi(1993) introduces a new goodness-of-fit statisticJ<sup>2</sup>, which has an asymptotic chi-squared distribution. However, the results of simulation indicate that the levels of significance are in general bigger than the nominal levels, which prompts us to device a version of J<sup>2</sup> statistic which would perform better under small sample size situations. We suggest adding 0.32 to each observed value and find that the adjustment indeed works rearonably well. This version of J^2 statistic is denoted as J(1)^2.   Although Pearson chi-square statistic X<sup>2</sup>, likelihood ratio statistic G<sup>2</sup>, Cresse-Read statistic I(2/3), J^2 and J(1) ^2 all have asymptotic chi-squared distributions, their small sample behaviors are not expected to be the same. Comparisons based on simulation studies are then made. The conclusions are as follows : (1) In terms of levels of significance, X<sup>2</sup> and I(2/3) behave more like a chi-squared distribution. Though J(1) ^2 does not perform as good as X<sup>2</sup> and I(2/3), it does outperform G<sup>2</sup> and J<sup>2</sup>. (2) In terms of powers, it does not seem that any of the test statistics has a clear advantage over the others.

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