Quasi shrinkage estimation of a block-structured covariance matrix

Abstract

In this paper, we study the estimation of a block covariance matrix with linearly structured off-diagonal blocks. We consider estimation based on the least squares method, which has some drawbacks. These estimates are not always well conditioned and may not even be definite. We propose a new estimation procedure providing a structured positive definite and well-conditioned estimator with good statistical properties. The least squares estimator is improved with the use of a shrinkage method and an additional algebraic approach. The resulting so-called quasi shrinkage estimator is compared with the structured maximum likelihood estimator.

Keywords:

• Covariance matrix
• block linear structure
• maximum likelihood estimation
• orthogonal projection
• shrinkage method

Disclosure statement

No potential conflict of interest was reported by the author(s).