Structural inference for high-dimensional covariance matrices

• Applicants: Professor Dr. Holger Dette; Professorin Dr. Angelika Rohde
• Subject Area: Mathematics
• Term: from 2012 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 197645397

We are concerned with estimation and inference for high-dimensional covariance matrices understructural constraints. We focus on banded matrices and matrices with a block diagonal structure.Structural constraints of this type induce a considerable complexity reduction which renders thestatistical procedures meaningful even if the dimension of the matrix is large as compared to thesample size. Key issue is a profound understanding of the spectral properties of correspondingestimators tailored to these sparsity constraints in order to perform efficient adaptive inference forhigh-dimensional data. Applications include volatility estimation in high-dimensional portfolios.

• DFG Programme: Research Units
• Subproject of: FOR 1735: Structural Inference in Statistics: Adaptation and Efficiency