Equivalent conditions for noncentral generalized Laplacianness and independence of matrix quadratic forms

  • Hu J
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Abstract

Let Y be an n × p multivariate normal random matrix with general covariance ΣY and W be a symmetric matrix. In the present article, the property that a matrix quadratic form Y′ WY is distributed as a difference of two independent (noncentral) Wishart random matrices is called the (noncentral) generalized Laplacianness (GL). Then a set of algebraic results are obtained which will give the necessary and sufficient conditions for the (noncentral) GL of a matrix quadratic form. Further, two extensions of Cochran's theorem concerning the (noncentral) GL and independence of a family of matrix quadratic forms are developed. © 2010 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Cochran's theorem
  • Independence
  • Kronecker product
  • Matrix quadratic forms
  • Noncentral Wishart distributions
  • Wishart distributions

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Authors

  • Jianhua Hu

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