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Language：Japanese   Publisher：Kansai University  

20030901-20040331

CiNii Books

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Kansai University Grant-in-Aid for the Faculty Joint Research Program 20010401-20020331

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二項分布に従うと仮定される観測データをもとに統計的推測を行う場合、大抵の教科書ではコンピュータの利用が必須である正確計算法よりむしろ、正規あるいはカイ自乗近似による方法に重点がおかれているのが普通である。このことに限らず、数理統計学の教科書では数値表の利用を前提とし、コンピュータの利用を考慮にいれていないのが普通である。その理由は、現在のようにコンピュータが一般学生に浸透していなかった頃(ほんの数年前)には、正確計算法についての説明を行っても計算不可能だったためである。しかし現在のコンピュータ環境を考えると、正確計算法に重点を置いたほうが好ましいように感じる。正確法はその言葉通り正確であり、近似理論を用いることがないので手続きに曖昧さがなくなるという利点を持っている。この研究レポートでは、対象を二項分布に限定し、その場合の統計的推測を正確法で行うための方法について述べる。なお、正確法の計算を行うためのソフトウェアは Mathematicaとする。

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We are going to compare the exact unconditional powers resulting from using three well known goodness-of-fit statistics, i.e., Pearson chi-squared statistic, deviance and power divergence statistic, in testing conditionally and exactly the equality of three binomial proportions. As far as I know, no paper has paid any attention to the selection of test statistics in the context of an exact conditional test. This is partly because almost all authors, apart from Mehta and Hilton (1993), have treated two binomial proportions, where signed root of each frequently used goodness-of -fit statistic is a monotonous functions of an observed value on a conditional reference set. Theoretical investigations are carried out and numerical results are obtained on various settings of binomial parameters.

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Language：Japanese   Publisher：Kansai University  

CiNii Books

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Kansai University Grant-in-Aid for the Faculty Joint Research Program 199704-199803

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Kansai University Grant-in-Aid for the Faculty Joint Research Program 199404-199503

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Grant-in-Aid for Encouragement of Young Scientists 199304-199403

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Language：Japanese   Publisher：Japanese Society of Computational Statistics  

The generalized linear models (in short GLM) proposed by Nelder and Wedderburn (1972) are generalization of classical linear model and include logistic linear model for proportions and log linear model for counts as typical examples. It seems that the success of GLM depends greatly on the fact that the theoretical and computational difficulties they caused are trivial relative to the generosity they gained. The notion of the quasi-likelihood proposed by Wedderburn (1974) has enlarged the applicability of GLM, thus, they have been extended in an analogous way as classical linear model and many techniques which are usefull in classical linear model have been adapted. In GLM, however, the results are less rigorous and less explicit. We can explain this problem as one of residual ; there is no quantity which is comparable to the residual in classical linear model. In this paper, we intend to clarify the issues comparing Pearson chi-squared statistic with deviance.

DOI： 10.20551/jscswabun.3.1_55

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文部省科研費

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