On Properties of the (I¦, a)-Power Divergence Family with Applications in Goodness of Fit Tests
On Properties of the (I¦, a)-Power Divergence Family with Applications in Goodness of Fit Tests
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DOI：
10.1007/s11009-010-9205-8
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发表时间：
2012-06-01
影响因子：
0.9
通讯作者：
Karagrigoriou, Alex
中科院分区：
文献类型：
--
作者：
Vonta, Filia;Mattheou, Kyriacos;Karagrigoriou, Alex
本文通过引入一类广义的散度测度，即（Ⅰ-破竖条，a）-幂散度族，统一了不同的散度测度，并研究了它的主要性质，包括极限性、保序性和二次收敛性.对于建议的措施类的实际影响，我们研究其使用的拟合优度检验多项式人口。特别是，一个测试统计量的拟合优度测试的基础上提出的家庭的措施进行了研究，小样本量和各种多项式分布，包括对称，偏态和等概率模型。建议的统计量似乎在所有情况下都很好地工作，而不是其他传统的测试，包括传统的卡方皮尔逊检验，这可能在某些情况下，但不是所有情况下都很好。
In this paper we unify the different measures of divergence by introducing a general class of measures of divergence, the (I broken vertical bar, a) -power divergence family and investigate its main properties including the limiting property, the order preserving property, and the quadratic convergence. For the practical implications of the proposed class of measures, we examine its use in goodness of fit tests for multinomial populations. In particular, a test statistic for goodness of fit tests based on the proposed family of measures is investigated for small sample sizes and various multinomial distributions that include symmetric, skewed and equiprobable models. The proposed statistic appears to work well in all cases considered as opposed to other traditional tests including the traditional chi-squared Pearson's test, which may work well in some but not all situations.