Structural inference for high-dimensional covariance matrices

高维协方差矩阵的结构推理

• 批准号: 213996264
• 负责人: Professor Dr. Holger Dette
• 金额: --
• 依托单位: Lehrstuhl Stochastik, insbesondere Statistik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/213996264?language=en
• 关键词: Structural; inference; dimensional; covariance; matrices

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.

我们关注的是结构约束下高维协方差矩阵的估计和推断。我们把重点放在带状矩阵和矩阵的块对角结构.这种类型的结构约束诱导相当大的复杂性降低，使统计过程的意义，即使矩阵的维数是大的相比，thesample大小.关键问题是深刻理解相应估计量的谱特性，以适应这些稀疏性约束，以便对高维数据进行有效的自适应推理。应用包括高维投资组合中的波动率估计。