Alexandre Belloni, Victor Chernozhukov, Christian Hansen
arXiv 31 Dec 2011 · Statistics — Methodology · 31 citations (OpenAlex)
arXiv:1201.0224 · PDF · DOI · OpenAlex · Extracted main text
We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances. Our analysis allows the number of controls to be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "post-double-selection" method. Our results apply to Lasso-type methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We illustrate the use of the developed methods with numerical simulations and an application to the effect of abortion on crime rates.
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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 | Donohue III and Levitt (2001) The Impact of Legalized Abortion on Crime | 1.000 | 20 | 3 | 100% |
| 2 | Belloni, Chen, Chernozhukov, and Hansen (2010) Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain | 0.950 | 7 | 4 | 86% |
| 3 | Bickel, Ritov, and Tsybakov (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.928 | 4 | 3 | 100% |
| 4 | Belloni and Chernozhukov (2011) Least Squares After Model Selection in High-dimensional Sparse Models | 0.909 | 8 | 6 | 75% |
| 5 | Cattaneo, Jansson, and Newey (2010) Alternative Asymptotics and the Partially Linear Model with Many Regressors | 0.874 | 5 | 2 | 100% |
| 6 | Foote and Goetz (2008) The Impact of Legalized Abortion on Crime: Comment | 0.811 | 4 | 2 | 100% |
| 7 | Rudelson and Zhou (2011) Reconstruction from anisotropic random measurements | 0.737 | 5 | 3 | 40% |
| 8 | Belloni, Chernozhukov, and Hansen (2011) Inference for High-Dimensional Sparse Econometric Models self | 0.737 | 3 | 2 | 100% |
| 9 | Candes and Tao (2007) The Dantzig selector: statistical estimation when p is much larger than n | 0.644 | 2 | 2 | 100% |
| 10 | Frank and Friedman (1993) A Statistical View of Some Chemometrics Regression Tools | 0.644 | 2 | 2 | 100% |
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