Debiased machine learning of global and local parameters using regularized Riesz representers
Name
1802.08667.pdf
Description
Submitted version
Size
455.7 KB
Format
Adobe PDF
Checksum (MD5)
19771e6cae964293a8e232f3cc3fb051
Author(s)
Chernozhukov, Victor
Newey, Whitney K
Singh, Rahul
Date Issued
2022
Journal
Econometrics Journal
Publisher
Oxford University Press (OUP)
Citation
Chernozhukov, Victor, Newey, Whitney K and Singh, Rahul. 2022. "Debiased machine learning of global and local parameters using regularized Riesz representers." Econometrics Journal.
Version
Original manuscript
Abstract
Summary
We provide adaptive inference methods, based on $\ell _1$ regularization, for regular (semiparametric) and nonregular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of nonregular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ‘double sparsity robustness’: either the approximation to the regression or the approximation to the representer can be ‘completely dense’ as long as the other is sufficiently ‘sparse’. Our main results are nonasymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.
We provide adaptive inference methods, based on $\ell _1$ regularization, for regular (semiparametric) and nonregular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of nonregular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ‘double sparsity robustness’: either the approximation to the regression or the approximation to the representer can be ‘completely dense’ as long as the other is sufficiently ‘sparse’. Our main results are nonasymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.
MIT Department
Massachusetts Institute of Technology. Department of Economics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1093/ECTJ/UTAC002
