Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598912 | Linear Algebra and its Applications | 2015 | 25 Pages |
Abstract
Concise formulae are given for the cumulant matrices of a real-valued (zero-mean) random vector up to order 6. In addition to usual matrix operations, they involve only the Kronecker product, the vec operator, and the commutation matrix. Orders 5 and 6 are provided here for the first time; the same method as provided in the paper can be applied to compute higher orders. An immediate consequence of these formulae is to return 1) upper bounds on the rank of the cumulant matrices and 2) the expression of the sixth-order moment matrix of a Gaussian vector. Due to their conciseness, the proposed formulae also have a computational advantage as compared to the repeated use of Leonov and Shiryaev formula.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hanany Ould-Baba, Vincent Robin, Jérôme Antoni,