Structural inference for high-dimensional covariance matrices

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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.