Denis Nekipelov, Vira Semenova, Vasilis Syrgkanis
arXiv 13 Jun 2018 · Mathematics — Statistics Theory · publishedEconometrics Journal (2021) · 9 citations (OpenAlex)
arXiv:1806.04823 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias, preserving the single index property. We then take the loss function to be an indefinite integral of the adjusted moment function with respect to the single index. The proposed Lasso estimator converges at the oracle rate, where the oracle knows the nuisance function and solves only the parametric problem. We demonstrate our method by estimating the short-term heterogeneous impact of Connecticut's Jobs First welfare reform experiment on women's welfare participation decision.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Negahban, S. N., P. Ravikumar, M. J. Wainwright, and B. Yu (2012, Nov) (2012) A unified framework for high-dimensional analysis of $m$-estimators with decomposable regularizers | 1.000 | 6 | 4 | 100% |
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| 3 | van der Geer, S., P. Bühlmann, Y. Ritov, and R. Dezeure (2014) On asymptotically optimal confidence regions and tests for high-dimensional models | 0.874 | 5 | 2 | 100% |
| 4 | Semenova, V., M. Goldman, V. Chernozhukov, and M. Taddy (2017, Decem… (2017) Estimation and inference about heterogeneous treatment effects in high-dimensional dynamic panels self | 0.737 | 3 | 2 | 100% |
| 5 | Ichimura, H (1993) Semiparametric least squares (sls) and weighted sls estimation of single-index models | 0.737 | 3 | 2 | 100% |
| 6 | Newey, W. (1994, November) (1994) The asymptotic variance of semiparametric estimators | 0.737 | 3 | 2 | 100% |
| 7 | Shalev-Shwartz, S. and S. Ben-David (2014) Understanding Machine Learning: From Theory to Algorithms | 0.737 | 3 | 2 | 100% |
| 8 | Chernozhukov, V., D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, W… (2018) Double/debiased machine learning for treatment and structural parameters | 0.737 | 3 | 2 | 100% |
| 9 | Klein, R. and R. Spady (1993) An efficient semiparametric estimator for binary response models | 0.737 | 3 | 2 | 100% |
| 10 | Chernozhukov, V., J. C. Escanciano, H. Ichimura, W. K. Newey, and J.… (2016) Locally Robust Semiparametric Estimation | 0.644 | 2 | 2 | 100% |
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