Structured Covariance Matrices and Unconstrained Parameterization

Wei Lan and Chih-Ling Tsai
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Wei Lan: Southwestern University of Finance and Economics, School of Statistics and Data Science and Center of Statistical Research
Chih-Ling Tsai: University of California - Davis, Graduate School of Management

Chapter Chapter 3 in Covariance Analysis and Beyond, 2026, pp 37-50 from Springer

Abstract: Abstract This chapter presents four structured covariance matricesStructured covariance matrices that indicate specific relationships among the multivariate responses. Then, it introduces linear covariance modelsLinear covariance models, which posit a linear relationship between the covariance matrix and a set of known symmetric matrices. To assure the covariance matrix is positive definite, two unconstrained parameterizationsUnconstrained parameterization are considered. In addition, four empirical examples are presented to illustrate the usefulness of structured covariance matricesStructured covariance matrices.

Date: 2026
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DOI: 10.1007/978-3-032-08796-6_3

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