A New Parametrization of Correlation Matrices
A New Parametrization of Correlation Matrices
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DOI：
10.3982/ecta16910
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发表时间：
2020-12
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影响因子：
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通讯作者：
Ilya Archakov;P. Hansen
中科院分区：
文献类型：
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作者：
Ilya Archakov;P. Hansen
我们引入了一种新颖的相关矩阵参数化。重新参数化有助于通过不受限制的向量对相关矩阵和协方差矩阵进行建模，其中正定性是一种固有属性。这种参数化可以被视为 Fisther Z 变换到更高维度的推广，并且具有广泛的潜在应用。提供了一种从任何 d 维向量（其中 d = n(n-1)/2）重建唯一 n x n 相关矩阵的算法，并推导出其数值复杂度。
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisther's Z-transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n x n correlation matrix from any d-dimensional vector (with d = n(n-1)/2) is provided, and we derive its numerical complexity.