A higher-order LQ decomposition for separable covariance models

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• 作者：David Gerard^a ; ^{gerard2@uw.edu" class="auth_mail" title="E-mail the corresponding author} ; Peter Hoff^a ; ^b ; ^{pdhoff@uw.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A69 ; 62H12 ; 62H15 ; 65F99
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：505
• 期：Complete
• 页码：57-84
• 全文大小：544 K

文摘

We develop a higher-order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the multilinear normal model. This role is analogous to that of the LQ decomposition in likelihood inference for the multivariate normal model. Additionally, this higher-order LQ decomposition can be used to construct an alternative version of the popular higher-order singular value decomposition for tensor-valued data. We also develop a novel generalization of the polar decomposition to tensor-valued data.