摘要翻译：
高斯图形模型最近在经济学中被用来获得Agent之间的依赖网络。GLASSO(Glatical Lasso，GLASSO)是一种广泛使用的估计方法，它是利用精确矩阵$\omega$上的$l_{1,1}$矩阵范数进行正则化的最大似然估计。$l_{1,1}$范数是一个套索惩罚，控制稀疏性，或$\omega$中的零的个数。我们提出了一个新的估计器，称为结构化图形套索(SGLASSO)，它使用$L_{1,2}$混合范数。在$\omega$中使用$l_{1,2}$罚控件来构造稀疏性。证明了在网络规模一定的情况下，SGLASSO渐近等价于一个优先考虑高次节点稀疏恢复的不可行GLASSO问题。Monte Carlo仿真表明，SGLASSO在估计整体精度矩阵和估计图形模型结构方面优于GLASSO。在一个经典的企业投资数据集的实证说明中，我们得到了一个表现出核心-外围结构的企业依赖网络，通用汽车、通用电气和美国钢铁构成了企业的核心群。
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英文标题：
《Estimation of Graphical Models using the $L_{1,2}$ Norm》
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作者：
Khai X. Chiong, Hyungsik Roger Moon
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最新提交年份：
2017
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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：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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英文摘要：
  Gaussian graphical models are recently used in economics to obtain networks of dependence among agents. A widely-used estimator is the Graphical Lasso (GLASSO), which amounts to a maximum likelihood estimation regularized using the $L_{1,1}$ matrix norm on the precision matrix $\Omega$. The $L_{1,1}$ norm is a lasso penalty that controls for sparsity, or the number of zeros in $\Omega$. We propose a new estimator called Structured Graphical Lasso (SGLASSO) that uses the $L_{1,2}$ mixed norm. The use of the $L_{1,2}$ penalty controls for the structure of the sparsity in $\Omega$. We show that when the network size is fixed, SGLASSO is asymptotically equivalent to an infeasible GLASSO problem which prioritizes the sparsity-recovery of high-degree nodes. Monte Carlo simulation shows that SGLASSO outperforms GLASSO in terms of estimating the overall precision matrix and in terms of estimating the structure of the graphical model. In an empirical illustration using a classic firms' investment dataset, we obtain a network of firms' dependence that exhibits the core-periphery structure, with General Motors, General Electric and U.S. Steel forming the core group of firms.
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PDF链接：
https://arxiv.org/pdf/1709.10038