A New Parametrization of Correlation Matrices

• Tác giả: Ilya Archakov, Peter Reinhard Hansen
• Ngôn ngữ: eng
• Ký hiệu phân loại: 512.897 Algebra
• Thông tin xuất bản: 2020
• Bộ sưu tập: Báo, Tạp chí
• ID: 165740

Tóm tắt

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.