英文标题：
《A Canonical Representation of Block Matrices with Applications to
Covariance and Correlation Matrices》
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作者：
Ilya Archakov and Peter Reinhard Hansen
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最新提交年份：
2021
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英文摘要：
We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix exponential. These results are particularly useful for block covariance and block correlation matrices, where evaluation of the Gaussian log-likelihood and estimation are greatly simplified. We illustrate this with an empirical application using a large panel of daily asset returns. Moreover, the representation paves new ways to regularizing large covariance/correlation matrices, test block structures in matrices, and estimate regressions with many variables.
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中文摘要：
我们得到了块矩阵的规范表示。这种表示法便于简单计算块矩阵的行列式、矩阵逆和其他幂，以及矩阵对数和矩阵指数。这些结果对于块协方差和块相关矩阵特别有用，在这些矩阵中，高斯对数似然和估计的计算大大简化。我们通过一个使用大量每日资产收益率的实证应用程序来说明这一点。此外，该表示为正则化大型协方差/相关矩阵、矩阵中的测试块结构以及估计多变量回归铺平了新的道路。
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分类信息：

一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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