Alexandre Belloni, Mingli Chen, Victor Chernozhukov
arXiv 1 Jul 2016 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2025) · 4 citations (OpenAlex)
arXiv:1607.00286 · PDF · DOI · OpenAlex · Extracted main text
We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by evaluating the distributional dependence structure at each quantile index. As such, CIQGMs can be used for validation of the graph structure in the causal graphical models (\cite{pearl2009causality, robins1986new, heckman2015causal}). One main advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. PQGMs characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. Because of QGMs' ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements. We develop estimation and inference methods for QGMs focusing on the high-dimensional case, where the number of variables in the graph is large compared to the number of observations. For CIQGMs, these methods and results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.
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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 | Alexandre Belloni and Victor Chernozhukov (2011) $_1$-penalized quantile regression for high dimensional sparse models self | 1.000 | 8 | 4 | 100% |
| 2 | Alexandre Belloni, Victor Chernozhukov, and Kengo Kato (2013) Robust inference in high-dimensional approximately sparse quantile regression models self | 1.000 | 8 | 4 | 100% |
| 3 | Aad van der Vaart and Jon Wellner (1996) Weak Convergence and Empirical Processes | 1.000 | 7 | 5 | 100% |
| 4 | Alexandre Belloni, Victor Chernozhukov, Ivan Fernández-Val, and Chri… (2017) Program evaluation and causal inference with high-dimensional data self | 1.000 | 5 | 3 | 100% |
| 5 | Victor Chernozhukov, Denis Chetverikov, and Kengo Kato (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors self | 1.000 | 5 | 3 | 100% |
| 6 | Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov, and Ying… (2015) Uniformly valid post-regularization confidence regions for many functional parameters in z-estimation framework self | 0.928 | 4 | 4 | 100% |
| 7 | Han Liu and Lie Wang (2017) Tiger: A tuning-insensitive approach for optimally estimating gaussian graphical models | 0.874 | 5 | 2 | 100% |
| 8 | Alexandre Belloni, Victor Chernozhukov, and Christian Hansen (2014) Inference on treatment effects after selection among high-dimensional controls self | 0.843 | 3 | 3 | 100% |
| 9 | Peter Bickel, Ya'acov Ritov, and Alexandre Tsybakov (2009) Simultaneous analysis of lasso and dantzig selector | 0.843 | 3 | 3 | 100% |
| 10 | Jerome Friedman, Trevor Hastie, and Robert Tibshirani (2008) Sparse inverse covariance estimation with the graphical lasso | 0.843 | 3 | 3 | 100% |
Showing the top 10 of 110 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Interpreting Quantile Independence | 0.405 | 1 | 1 |
| 2 | 1 Recovering Network Structure from Aggregated Relational Data using Penalized Regression | 0.405 | 1 | 1 |
| 3 | Choosing Exogeneity Assumptions in Potential Outcome Models | 0.405 | 1 | 1 |