Structural inference for high-dimensional covariance matrices

我们关注结构约束下高维协方差矩阵的估计和推理。我们主要研究带状矩阵和具有块对角结构的矩阵。这种类型的结构约束导致相当大的复杂性降低，这使得统计程序有意义，即使矩阵的维数与样本量相比很大。关键问题是深刻理解为这些稀疏性约束量身定制的相应估计器的谱特性，以便对高维数据执行有效的自适应推理。应用包括高维投资组合的波动率估计。

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.