Small-Sample Comparisons for the Power Divergence Goodness-of-Fit Statistics
Small-Sample Comparisons for the Power Divergence Goodness-of-Fit Statistics
复制标题
功率散度拟合优度统计的小样本比较
DOI：
10.1080/01621459.1984.10477113
复制
发表时间：
1984
影响因子：
3.7
通讯作者：
Timothy R. C. Read
中科院分区：
文献类型：
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作者：
Timothy R. C. Read
本文研究了拟合优度统计量幂发散族的小样本性质。使用渐近χ2和三个替代近似值来获得适当的检验水平，以与精确水平进行比较。结果表明，若采用χ2近似，则对数似然比G2有许多较好的统计量（包括Pearson的χ2）.此外，在特定的替代对称零假设下的精确功效比较表明，基于G2和χ2的众所周知的检验的功效可以通过从该家族中选择其他统计量来提高。提出了一个解释的观察和预期计数之间的相对偏差的影响。
Abstract The small-sample properties of the power divergence family of goodness-of-fit statistics (Cressie and Read in press) are examined. The asymptotic χ2 and three alternative approximations are used to obtain appropriate test levels for comparison with the exact level. It is shown that if the χ2 approximation is to be used, then there are many preferable statistics to the log-likelihood ratio G 2 (including Pearson's χ2). Furthermore, exact power comparisons under specific alternatives to the symmetric null hypothesis show that the power of the well-known tests based on G 2 and χ2 can be improved by choosing other statistics from the family. An explanation is proposed in terms of the effect of relative deviations between observed and expected counts.