Moments of the Fisher Transform: Applications Using Small Samples
Moments of the Fisher Transform: Applications Using Small Samples
复制标题
Fisher 变换的矩：使用小样本的应用
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
J. H. Steiger
中科院分区：
文献类型：
--
作者：
R. Fouladi;S. Marani;J. H. Steiger
本文提出了一种理论发展，扩展了样本相关系数分布和Fisher变换（Fisher，1921）的结果。几个著名的相关程序使用Fisher变换或其平方作为假设检验的基础。这些过程假设Fisher变换的方差可以近似为1/（3）n-。我们目前的结果表明，对于小样本量，这不一定是真的。我们目前的结果表明，对于小样本量，这不一定是真的。对于小n（≤ 20）的零相关和非零相关，计算Fisher变换及其平方的精确矩。推广了Hotelling（Hotelling，1953）关于Fisher变换及其平方的矩的经典级数展开式，并与Fisher变换及其平方的精确矩进行了比较.蒙特卡罗实验被用来证明这些结果可能会产生显着的改善，在小样本的相关矩阵的模式假设的测试性能。
This paper presents a theoretical development that extends results on the distribution of the sample correlation coefficient and the Fisher transform (Fisher, 1921). Several well known correlational procedures use the Fisher transform or its square as the basis of hypothesis testing. These procedures assume that the variance of the Fisher transform can be approximated adequately as 1/(3) n −. We present results that demonstrate that for small sample size this is not necessarily true. We present results that demonstrate that for small sample size this is not necessarily true. Exact moments of the Fisher transform and its square are computed for both null and non-null correlations for small n (≤ 20). An extension of the classic series expansion formulae of Hotelling (Hotelling, 1953) for the moments of the Fisher transform and its square are discussed and compared with the exact moments of the Fisher transform and its square. Monte Carlo experiments are used to demonstrate how these results may produce significant improvements in the small sample performance of tests for pattern hypothesis on correlation matrices.