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Non-Parametric Inference Adaptive to Intrinsic Dimension

Author

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  • Khashayar Khosravi
  • Greg Lewis
  • Vasilis Syrgkanis

Abstract

We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic dimension $d$, as measured by locally low doubling measures. Our estimation is based on a sub-sampled ensemble of the $k$-nearest neighbors ($k$-NN) $Z$-estimator. We show that if the intrinsic dimension of the covariate distribution is equal to $d$, then the finite sample estimation error of our estimator is of order $n^{-1/(d+2)}$ and our estimate is $n^{1/(d+2)}$-asymptotically normal, irrespective of $D$. The sub-sampling size required for achieving these results depends on the unknown intrinsic dimension $d$. We propose an adaptive data-driven approach for choosing this parameter and prove that it achieves the desired rates. We discuss extensions and applications to heterogeneous treatment effect estimation.

Suggested Citation

  • Khashayar Khosravi & Greg Lewis & Vasilis Syrgkanis, 2019. "Non-Parametric Inference Adaptive to Intrinsic Dimension," Papers 1901.03719, arXiv.org, revised Jun 2019.
  • Handle: RePEc:arx:papers:1901.03719
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    References listed on IDEAS

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    1. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Stefan Wager & Susan Athey, 2018. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1228-1242, July.
    4. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    5. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney K. Newey, 2016. "Double machine learning for treatment and causal parameters," CeMMAP working papers 49/16, Institute for Fiscal Studies.
    6. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    7. Lester Mackey & Vasilis Syrgkanis & Ilias Zadik, 2017. "Orthogonal Machine Learning: Power and Limitations," Papers 1711.00342, arXiv.org, revised Aug 2018.
    8. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    9. Sendhil Mullainathan & Jann Spiess, 2017. "Machine Learning: An Applied Econometric Approach," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 87-106, Spring.
    10. Lewbel, Arthur, 2007. "A local generalized method of moments estimator," Economics Letters, Elsevier, vol. 94(1), pages 124-128, January.
    11. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    12. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    13. A. Belloni & V. Chernozhukov & I. Fernández‐Val & C. Hansen, 2017. "Program Evaluation and Causal Inference With High‐Dimensional Data," Econometrica, Econometric Society, vol. 85, pages 233-298, January.
    14. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    15. Victor Chernozhukov & Denis Nekipelov & Vira Semenova & Vasilis Syrgkanis, 2018. "Plug-in regularized estimation of high dimensional parameters in nonlinear semiparametric models," CeMMAP working papers CWP41/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    17. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    18. Denis Nekipelov & Vira Semenova & Vasilis Syrgkanis, 2018. "Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models," Papers 1806.04823, arXiv.org, revised Sep 2021.
    19. Reiss, Peter C. & Wolak, Frank A., 2007. "Structural Econometric Modeling: Rationales and Examples from Industrial Organization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 64, Elsevier.
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    Cited by:

    1. Nathan Kallus & Miruna Oprescu, 2022. "Robust and Agnostic Learning of Conditional Distributional Treatment Effects," Papers 2205.11486, arXiv.org, revised Feb 2023.
    2. Qizhao Chen & Vasilis Syrgkanis & Morgane Austern, 2022. "Debiased Machine Learning without Sample-Splitting for Stable Estimators," Papers 2206.01825, arXiv.org, revised Nov 2022.
    3. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2020. "Adversarial Estimation of Riesz Representers," Papers 2101.00009, arXiv.org, revised Jan 2024.
    4. Andrew Bennett & Nathan Kallus, 2020. "Efficient Policy Learning from Surrogate-Loss Classification Reductions," Papers 2002.05153, arXiv.org.
    5. Krikamol Muandet & Wittawat Jitkrittum & Jonas Kubler, 2020. "Kernel Conditional Moment Test via Maximum Moment Restriction," Papers 2002.09225, arXiv.org, revised Jun 2020.

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