ASYMPTOTIC EXPANSIONS OF THE DISTRIBUTION OF THE ESTIMATOR FOR THE GENERALIZED PARTIAL CORRELATION UNDER NONNORMALITY
ASYMPTOTIC EXPANSIONS OF THE DISTRIBUTION OF THE ESTIMATOR FOR THE GENERALIZED PARTIAL CORRELATION UNDER NONNORMALITY
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DOI：
10.2333/bhmk.35.15
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
H. Ogasawara
中科院分区：
文献类型：
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作者：
H. Ogasawara
广义偏相关被定义为两个变量之间的相关，其中共同和独特的第三变量的线性效应从两个变量中偏出。广义偏相关包括作为特殊情况的简单相关、偏相关、部分/半偏相关和双部分相关。在非正态性下，广义偏相关的标准化样本系数分布的埃奇沃斯展开高达 O(1/n) 阶。还使用 Edgeworth 展开、Cornish-Fisher 展开和具有变量变换的 Hall 方法获得了 Studentized 估计量分布的渐近展开。作为扩展，给出了多变量情况或广义部分集相关的结果。
The generalized partial correlation is denned as a correlation between two variables, where the linear effects of common and unique third variables are partialed out from the two variables. The generalized partial correlation includes simple, partial, part/semipartial and bipartial correlations as special cases. The Edgeworth expansion of the distribution of the standardized sample coefficient for the generalized partial correlation is obtained up to order O(1/n) under nonnormality. Also asymptotic expansions of the distribution of the Studentized estimator are obtained using the Edgeworth expansion, Cornish-Fisher expansion and Hall’s method with variable transformation. As extensions, the results of multivariate cases or generalized partial set-correlations are given.