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New $\sqrt{n}$-consistent, numerically stable higher-order influence function estimators

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  • Lin Liu
  • Chang Li

Abstract

Higher-Order Influence Functions (HOIFs) provide a unified theory for constructing rate-optimal estimators for a large class of low-dimensional (smooth) statistical functionals/parameters (and sometimes even infinite-dimensional functions) that arise in substantive fields including epidemiology, economics, and the social sciences. Since the introduction of HOIFs by Robins et al. (2008), they have been viewed mostly as a theoretical benchmark rather than a useful tool for statistical practice. Works aimed to flip the script are scant, but a few recent papers Liu et al. (2017, 2021b) make some partial progress. In this paper, we take a fresh attempt at achieving this goal by constructing new, numerically stable HOIF estimators (or sHOIF estimators for short with ``s'' standing for ``stable'') with provable statistical, numerical, and computational guarantees. This new class of sHOIF estimators (up to the 2nd order) was foreshadowed in synthetic experiments conducted by Liu et al. (2020a).

Suggested Citation

  • Lin Liu & Chang Li, 2023. "New $\sqrt{n}$-consistent, numerically stable higher-order influence function estimators," Papers 2302.08097, arXiv.org.
    • Handle: RePEc:arx:papers:2302.08097
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    References listed on IDEAS

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    4. Rajarshi Mukherjee & Whitney K. Newey & James Robins, 2017. "Semiparametric efficient empirical higher order influence function estimators," CeMMAP working papers 30/17, Institute for Fiscal Studies.
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    8. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
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