Alexandre Belloni, Victor Chernozhukov, Christian Hansen
arXiv 31 Dec 2011 · Statistics — Methodology · 75 citations (OpenAlex)
arXiv:1201.0220 · PDF · DOI · OpenAlex · Extracted main text
This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the regression function is well-approximated by a parsimonious, yet unknown set of regressors. The latter condition makes it possible to estimate the entire regression function effectively by searching for approximately the right set of regressors. We discuss methods for identifying this set of regressors and estimating their coefficients based on $\ell_1$-penalization and describe key theoretical results. In order to capture realistic practical situations, we expressly allow for imperfect selection of regressors and study the impact of this imperfect selection on estimation and inference results. We focus the main part of the article on the use of HDS models and methods in the instrumental variables model and the partially linear model. We present a set of novel inference results for these models and illustrate their use with applications to returns to schooling and growth regression.
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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 | Belloni and Chernozhukov (2011) Least Squares After Model Selection in High-dimensional Sparse Models | 0.928 | 5 | 3 | 80% |
| 2 | Belloni and Chernozhukov (2011) $_1$-Penalized Quantile Regression for High Dimensional Sparse Models | 0.874 | 6 | 2 | 100% |
| 3 | van de Geer (2008) High-dimensional generalized linear models and the lasso | 0.874 | 5 | 2 | 100% |
| 4 | Gautier and Tsybakov (2011) High-dimensional Instrumental Variables Rergession and Confidence Sets | 0.843 | 3 | 3 | 100% |
| 5 | Belloni, Chen, Chernozhukov, and Hansen (2010) Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain | 0.811 | 4 | 2 | 100% |
| 6 | Hansen, Hausman, and Newey (2008) Estimation with Many Instrumental Variables | 0.811 | 4 | 2 | 100% |
| 7 | Newey (1997) Convergence Rates and Asymptotic Normality for Series Estimators | 0.811 | 4 | 2 | 100% |
| 8 | Bickel, Ritov, and Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.737 | 3 | 2 | 100% |
| 9 | Angrist and Krueger (1991) Does Compulsory School Attendance Affect Schooling and Earnings? | 0.693 | 5 | 1 | 100% |
| 10 | Barro and Sala-i-Martin (1995) Economic Growth | 0.693 | 5 | 1 | 100% |
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