论文标题
矩阵矩中的真实，双重相关的代数概括
Matrix Moments in a Real, Doubly Correlated Algebraic Generalization of the Wishart Model
论文作者
论文摘要
随着各种类型的复杂系统的大量数据的增长，随机协方差或相关矩阵的WishART模型继续发现更多的应用。沉重的尾巴经常遇到Wishart模型的迅速概括，涉及代数分布而不是高斯。数学特性提出了新的挑战，尤其是对于双重相关的版本。在这里，我们研究了实际协方差或相关矩阵的双重相关代数模型。我们专注于矩阵矩，并明确计算第一个和第二个，后者的计算是不平凡的。我们通过将问题与AOMOTO积分相关联并扩展递归技术来计算Ingham-Siegel积分来解决该问题。我们将结果与高斯案例进行了比较。
The Wishart model of random covariance or correlation matrices continues to find ever more applications as the wealth of data on complex systems of all types grows. The heavy tails often encountered prompt generalizations of the Wishart model, involving algebraic distributions instead of a Gaussian. The mathematical properties pose new challenges, particularly for the doubly correlated versions. Here we investigate such a doubly correlated algebraic model for real covariance or correlation matrices. We focus on the matrix moments and explicitly calculate the first and the second one, the computation of the latter is non-trivial. We solve the problem by relating it to the Aomoto integral and by extending the recursive technique to calculate Ingham-Siegel integrals. We compare our results with the Gaussian case.
