On estimation of a partitioned covariance matrix with linearly structured blocks

Katarzyna Filipiak (), Augustyn Markiewicz (), Adam Mieldzioc () and Malwina Mrowińska ()
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Katarzyna Filipiak: Poznan University of Technology
Augustyn Markiewicz: Poznan University of Life Sciences
Adam Mieldzioc: Poznan University of Life Sciences
Malwina Mrowińska: Poznan University of Technology

Statistical Papers, 2025, vol. 66, issue 4, No 25, 26 pages

Abstract: Abstract The aim of this paper is to introduce an estimation method for a linearly structured partitioned covariance matrix. In contrast to well known linear structures of partitioned matrices, for example block compound symmetry, we allow the diagonal blocks of the covariance matrix to be of different dimensions. We adapt the shrinkage method to improve the properties of the projection of the sample covariance matrix onto the linear structure space. As spaces of target matrices, we choose various quadratic subspaces of structure space. This is a novel approach in the context of the structure space under consideration, and as a result a positive definite and well-conditioned estimator having the desired structure is determined. It is also shown that the statistical and algebraic properties of the estimator depend on the choice of target space.

Keywords: Multivariate model; Covariance structure; Least squares estimation; Projection; Shrinking; Quadratic subspace; 62H10; 62H12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01718-6

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