Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach
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Author(s)
Chernozhukov, Victor
Chernozhukov, Victor V
Date Issued
August 2015
Journal
Annual Review of Economics
Publisher
Annual Reviews
Citation
Chernozhukov, Victor et al. “Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach.” Annual Review of Economics 7, 1 (August 2015): 649–688
Version
Author's final manuscript
Abstract
We present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter in the presence of a very high-dimensional nuisance parameter that is estimated using selection or regularization methods. Our analysis provides a set of high-level conditions under which inference for the low-dimensional parameter based on testing or point estimation methods will be regular despite selection or regularization biases occurring in the estimation of the high-dimensional nuisance parameter. A key element is the use of so-called immunized or orthogonal estimating equations that are locally insensitive to small mistakes in the estimation of the high-dimensional nuisance parameter. As an illustration, we analyze affine-quadratic models and specialize these results to a linear instrumental variables model with many regressors and many instruments. We conclude with a review of other developments in post-selection inference and note that many can be viewed as special cases of the general encompassing framework of orthogonal estimating equations provided in this article. Keywords: Neyman; orthogonalization; C(α) statistics; optimal instrument; optimal score; optimal moment; efficiency; optimality
MIT Department
Massachusetts Institute of Technology. Department of Economics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1146/ANNUREV-ECONOMICS-012315-015826
