Covariance reducing models: An alternative to spectral modelling of covariance matrices
协方差约简模型：协方差矩阵谱建模的替代方法
We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covariance matrices to an informational core that is sufficient to characterize the variance heterogeneity among the populations. They possess useful equivariance properties and provide a clear alternative to spectral models for covariance matrices.