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Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models

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  • Denis Nekipelov
  • Vira Semenova
  • Vasilis Syrgkanis

Abstract

This paper contributes to the literature on high-dimensional sparse M-estimation by allowing the loss function to depend on a functional nuisance parameter, which we estimate by modern machine learning tools. For a class of single-index conditional moment restrictions (CMRs), we explicitly derive the loss function. We first adjust the moment function so that the gradient of the future M-estimator loss is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias. We then take the loss function to be an indefinite integral of the adjusted moment function with respect to the single-index. The proposed l1-regularized M-estimator achieves the oracle convergence rate, where the oracle knows the nuisance parameter and solves only the parametric problem. Our framework nests a novel approach to modeling heterogeneous treatment effects with a binary dependent variable. In addition, we apply our results to conditional moment models with missing data and static games of incomplete information. Finally, we generalize our results to generic extremum estimation with a nuisance component.

Suggested Citation

  • Denis Nekipelov & Vira Semenova & Vasilis Syrgkanis, 2018. "Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models," Papers 1806.04823, arXiv.org, revised Oct 2020.
  • Handle: RePEc:arx:papers:1806.04823
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    File URL: http://arxiv.org/pdf/1806.04823
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    References listed on IDEAS

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    1. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Sepanski, J. H. & Carroll, R. J., 1993. "Semiparametric quasilikelihood and variance function estimation in measurement error models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 223-256, July.
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    Cited by:

    1. Dylan J. Foster & Vasilis Syrgkanis, 2019. "Orthogonal Statistical Learning," Papers 1901.09036, arXiv.org, revised Sep 2020.
    2. Khashayar Khosravi & Greg Lewis & Vasilis Syrgkanis, 2019. "Non-Parametric Inference Adaptive to Intrinsic Dimension," Papers 1901.03719, arXiv.org, revised Jun 2019.
    3. Sookyo Jeong & Hongseok Namkoong, 2020. "Robust Causal Inference Under Covariate Shift via Worst-Case Subpopulation Treatment Effects," Papers 2007.02411, arXiv.org, revised Jul 2020.

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