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Improvement of test in contingency tables based on asymptotic approximation.

基于渐近逼近的列联表检验的改进。

基本信息

批准号：
16500168
负责人：
TANNICHI Nobuhiro
金额：
$ 1.92万
依托单位：
Kagoshima University (2006)Obihiro University of Agriculture and Veterinary Medicine (2004-2005)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

1. In the case that r X s contingency table is considered as full multinomial model, we derive expression of asymptotic expansion for the distribution of the test statistics based on Φ-divergence under independent null hypothesis. The expression consists of continuous and discontinuous terms. Evaluation for the continuous and discontinuous term is also considered. Using the term of asymptotic expansion assuming a continuous distribution in the expression, we construct transformation for improving small-sample accuracy of chi-square approximation of the distribution of the statistic under independent hypothesis.2. In the case that r X s contingency table is considered as product multinomial model, we derive expression of asymptotic expansion for the distribution of the test statistics based on power-divergence under null hypothesis that all of the multinomial populations are homogeneity. The expression consists of continuous and discontinuous terms. Evaluation for the continuous and discontinuous term is also considered when the number of samples from each population is the same.3. In the test of independence in full multinomial model, by assuming the continuity of the random variables, we derive asymptotic expansions for the distribution of the test statistics based on power-divergence under local alternative and non-local alternative hypotheses, respectively.

1.在r × s列联表为完全多项式模型的情况下，在独立原假设下，得到了检验统计量基于Φ-散度分布的渐近展开式.该表达式由连续项和不连续项组成。还考虑了连续项和不连续项的评估。利用表达式中假设连续分布的渐近展开项，构造了在独立假设下提高统计量分布的卡方逼近的小样本精度的变换.在r × s列联表为乘积多项式模型的情况下，在多项式总体均为齐次的原假设下，得到了检验统计量基于幂离的分布的渐近展开式.该表达式由连续项和不连续项组成。当每个总体的样本数相同时，也考虑了连续项和不连续项的评价.在完全多项模型的独立性检验中，通过假设随机变量连续，分别在局部备择假设和非局部备择假设下，得到了检验统计量分布基于幂离的渐近展开式.