Chiu, Tom Y. M.; Leonard, Tom; Tsui, Kam-Wah The matrix-logarithmic covariance model. (English) Zbl 0870.62043 J. Am. Stat. Assoc. 91, No. 433, 198-210 (1996). Summary: A flexible method is introduced to model the structure of a covariance matrix \({\mathcal C}\) and study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix \({\mathcal A}\), the matrix exponential transformation, \({\mathcal C}=\exp({\mathcal A})\), is a positive definite matrix. Because there is no constraint on the possible values of the upper triangular elements on \({\mathcal A}\), any possible structure of interest can be imposed on them. The method presented here is not intended to replace the existing special models available for a covariance matrix, but rather to provide a broad range of further structures that supplements existing methodology. Maximum likelihood estimation procedures are used to estimate the parameters, and the large-sample asymptotic properties are obtained. A simulation study and two real-life examples are given to illustrate the method introduced. Cited in 53 Documents MSC: 62H12 Estimation in multivariate analysis 62J12 Generalized linear models (logistic models) 15A99 Basic linear algebra Keywords:maximum likelihood estimation procedures; Golden-Thompson inequality; Volterra integral equation; covariance matrix; explanatory variables; matrix exponential transformation; large-sample asymptotic properties; simulation study PDFBibTeX XMLCite \textit{T. Y. M. Chiu} et al., J. Am. Stat. Assoc. 91, No. 433, 198--210 (1996; Zbl 0870.62043) Full Text: DOI