Structural inference for high-dimensional covariance matrices

我们主要研究结构约束下高维协方差矩阵的估计和推断。我们主要研究带状矩阵和具有块对角线结构的矩阵，这种类型的结构约束导致了相当大的复杂性降低，这使得统计过程即使在矩阵的维度比样本大的情况下也是有意义的。为了对高维数据进行有效的自适应推断，关键问题是要深刻理解相应估计器的谱特性，以适应这些稀疏性约束。应用包括高维投资组合中的波动率估计。

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.