Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data

Abstract

Modern investigation techniques (e.g., metabolomic, proteomic, lipidomic, genomic, transcriptomic, phenotypic), allow to collect high-dimensional data, where the number of observations is smaller than the number of features. In such cases, for statistical analyzing, standard methods cannot be applied or lead to ill-conditioned estimators of the covariance matrix. To analyze the data, we need an estimator of the covariance matrix with good properties (e.g., positive definiteness), and therefore covariance matrix identification is crucial. The paper presents an approach to determine the block-structured estimator of the covariance matrix based on an example of metabolomic data on the drought resistance of barley. This method can be used in many fields of science, e.g., in agriculture, medicine, food and nutritional sciences, toxicology, functional genomics and nutrigenomics.

Keywords

• covariance structure
• compound symmetry matrix
• first-order autoregression matrix
• Toeplitz matrix
• estimation
• structure identification