Estimation of a common covariance matrix for multiple classes with applications in meta- and discriminant analysis

We propose a hierarchical random effects model for a common covariance matrix in cases where multiple classes are present. It is applicable where the classes are believed to share a common covariance matrix of interest obscured by class-dependent noise. As such, it provides a basis for integrative or meta-analysis of covariance matrices where the classes are formed by datasets. Our approach is inspired by traditional meta-analysis using random effects models but the model is also shown to be applicable as an intermediate between linear and quadratic discriminant analysis. We derive basic properties and estimators of the model and compare their properties. Simple inference and interpretation of the introduced parameter measuring the inter-class homogeneity is suggested.