AN ASYMPTOTIC APPROXIMATION FOR THE DISTRIBUTION OF φ-DIVERGENCE MULTINOMIAL GOODNESS-OF-FIT STATISTIC UNDER LOCAL ALTERNATIVES
AN ASYMPTOTIC APPROXIMATION FOR THE DISTRIBUTION OF φ-DIVERGENCE MULTINOMIAL GOODNESS-OF-FIT STATISTIC UNDER LOCAL ALTERNATIVES
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局部备选方案下φ-散度多项拟合优度统计量分布的渐近逼近
DOI：
10.14490/jjss1995.31.207
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
A. Suzukawa
中科院分区：
文献类型：
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作者：
Nobuhiro Taneichi;Yuri Sekiya;A. Suzukawa
关于多项分布的拟合优度检验，Zografos等人。(1990)提出了φ-散度统计族，它将幂散度统计族作为特例包括在内。他们证明了在零假设下，φ散度统计族的成员都具有渐近等价的卡方分布。此外，Menendez等人。(1997)给出了φ散度统计量零分布的渐近展开式。本文给出了局部方案下φ-散度统计量分布的一个近似表达式。该近似是基于φ散度统计量分布的渐近展开式的连续项。利用这种近似方法，我们提出了一种新的统计量幂的近似。这些结果是Taneichi等人的结果的推广。讨论了功率发散统计问题。我们用数值方法研究了两种具体的φ散度统计量应用时的近似精度。通过数值研究，我们发现该近似比其他近似具有更好的性能。
On the goodness-of-fit test for multinomial distribution, Zografos et al. (1990) proposed the φ-divergence family of statistics, which includes the power divergence family of statistics as a special case. They showed that under null hypothesis, the members of the φ-divergence family of statistics all have an asymptotically equivalent chi-square distribution. Furthermore, Menendez et al. (1997) derived an asymptotic expansion for the null distribution of the φ-divergence statistic. In this paper, we derive an approximation for the distribution of the φ-divergence statistic under local alternatives. The approximation is based on the continuous term of the asymptotic expansion for the distribution of the φ-divergence statistic. By using the approxi- mation, we propose a new approximation for the power of the statistic. The results are generalizations of those derived by Taneichi et al. which discussed the power divergence statistic. We numerically investigate the accuracy of the approximation when two types of concrete φ-divergence statistics are applied. By the numerical investigation, we find that the present approximation performs better than the other approximations.