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Semiparametric efficient empirical higher order influence function estimators

Author

Listed:
  • Rajarshi Mukherjee

    (Institute for Fiscal Studies)

  • Whitney K. Newey

    (Institute for Fiscal Studies and MIT)

  • James Robins

    (Institute for Fiscal Studies)

Abstract

Robins et al. (2008, 2016b) applied the theory of higher order infuence functions (HOIFs) to derive an estimator of the mean of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous covariates; their estimator, in contrast to previous estimators, is semiparametric efficient under minimal conditions. However the Robins et al. (2008, 2016b) estimator depends on a non-parametric estimate of the density of X. In this paper, we introduce a new HOIF estimator that has the same asymptotic properties as their estimator but does not require non-parametric estimation of a multivariate density, which is important because accurate estimation of a high dimensional density is not feasible at the moderate sample sizes often encountered in applications. We also show that our estimator can be generalized to the entire class of functionals considered by Robins et al. (2008) which include the average effect of a treatment on a response Y when a vector X suffices to control confounding and the expected conditional variance of a response Y given a vector X.

Suggested Citation

  • Rajarshi Mukherjee & Whitney K. Newey & James Robins, 2017. "Semiparametric efficient empirical higher order influence function estimators," CeMMAP working papers CWP30/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:30/17
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    Citations

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    Cited by:

    1. Vladimir Koltchinskii & Mayya Zhilova, 2021. "Estimation of Smooth Functionals of Location Parameter in Gaussian and Poincaré Random Shift Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 569-596, August.
    2. Yiyan Huang & Cheuk Hang Leung & Xing Yan & Qi Wu & Shumin Ma & Zhiri Yuan & Dongdong Wang & Zhixiang Huang, 2022. "Robust Causal Learning for the Estimation of Average Treatment Effects," Papers 2209.01805, arXiv.org.
    3. Eric J. Tchetgen Tchetgen, 2022. "Eric J Tchetgen Tchetgen’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 723-725, July.
    4. Juan Carlos Escanciano & Joel Robert Terschuur, 2022. "Machine Learning Inference on Inequality of Opportunity," Papers 2206.05235, arXiv.org, revised Oct 2023.
    5. Shi, Chengchun & Xu, Tianlin & Bergsma, Wicher & Li, Lexin, 2021. "Double generative adversarial networks for conditional independence testing," LSE Research Online Documents on Economics 112550, London School of Economics and Political Science, LSE Library.
    6. Lin Liu & Chang Li, 2023. "New $\sqrt{n}$-consistent, numerically stable higher-order influence function estimators," Papers 2302.08097, arXiv.org.

    More about this item

    Keywords

    Higher Order In?uence Functions; Doubly Robust Functionals; Semiparametric E?ciency; Higher Order U-Statistics;
    All these keywords.

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