Khai X. Chiong, Hyungsik Roger Moon
arXiv 28 Sep 2017 · Econometrics
arXiv:1709.10038 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Yuan, M. and Y. Lin (2007) Model selection and estimation in the gaussian graphical model | 0.950 | 7 | 4 | 86% |
| 2 | Hastie, T., R. Tibshirani, and M. Wainwright (2015) Statistical learning with sparsity | 0.737 | 3 | 2 | 100% |
| 3 | Banerjee, O., L. El Ghaoui, and A. d'Aspremont (2008) Model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data | 0.737 | 3 | 2 | 100% |
| 4 | Friedman, J., T. Hastie, and R. Tibshirani (2008) Sparse inverse covariance estimation with the graphical lasso | 0.737 | 3 | 2 | 100% |
| 5 | Rothman, A. J., P. J. Bickel, E. Levina, and J. Zhu (2008) Sparse permutation invariant covariance estimation | 0.644 | 2 | 2 | 100% |
| 6 | Cai, T. T., W. Liu, H. H. Zhou, et al (2016) Estimating sparse precision matrix: Optimal rates of convergence and adaptive estimation | 0.511 | 2 | 1 | 100% |
| 7 | Greene, W. H (2012) Econometric analysis\/ (7th ed.) | 0.511 | 2 | 1 | 100% |
| 8 | Lam, C. and J. Fan (2009) Sparsistency and rates of convergence in large covariance matrix estimation | 0.511 | 2 | 1 | 100% |
| 9 | Acemoglu, D., V. M. Carvalho, A. Ozdaglar, and A. Tahbaz-Salehi (2012) The network origins of aggregate fluctuations | 0.405 | 1 | 1 | 100% |
| 10 | Baltagi, B (2008) Econometric analysis of panel data | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 91 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Quantile Graphical Models: Prediction and Conditional Independence with Applications to Systemic Risk | 0.405 | 1 | 1 |