A higher-order LQ decomposition for separable covariance models

TL;DR

This paper introduces a higher-order LQ decomposition for tensor data, enhancing likelihood-based inference in separable covariance models and offering new tools for tensor analysis.

Contribution

It develops a novel higher-order LQ decomposition and a tensor polar decomposition, advancing methods for likelihood inference and tensor data analysis.

Findings

Provides a new higher-order LQ decomposition for tensors

Enables alternative tensor SVD for separable covariance models

Introduces a tensor polar decomposition

Abstract

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.