×

The matrix-logarithmic covariance model. (English) Zbl 0870.62043

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.

MSC:

62H12 Estimation in multivariate analysis
62J12 Generalized linear models (logistic models)
15A99 Basic linear algebra
PDFBibTeX XMLCite
Full Text: DOI