arXiv 16 Feb 2023 · Mathematics — Statistics Theory
arXiv:2302.08097 · PDF · DOI · OpenAlex · Extracted main text
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).
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Lin Liu, Rajarshi Mukherjee, and James M Robins (2020) On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning self | 1.000 | 19 | 7 | 100% |
| 2 | Lin Liu, Rajarshi Mukherjee, Whitney K Newey, and James M Robins (2017) Semiparametric efficient empirical higher order influence function estimators self | 1.000 | 19 | 5 | 100% |
| 3 | James Robins, Lingling Li, Eric Tchetgen Tchetgen, and Aad van der V… (2016) Technical report: Higher order influence functions and minimax estimation of nonlinear functionals | 1.000 | 16 | 4 | 100% |
| 4 | Lin Liu, Rajarshi Mukherjee, and James M Robins (2021) Can we tell if the justification of the validity of wald confidence intervals of doubly robust functionals may be incorrect, wit… self | 1.000 | 14 | 6 | 100% |
| 5 | Kerollos Wanis, Lin Liu, Nelya Melnitchoukc, and James M Robins (2023) Machine learning and causal inference: Quantifying bias using higher order influence functions self | 1.000 | 8 | 4 | 100% |
| 6 | Andrea Rotnitzky, Ezequiel Smucler, and James M Robins (2021) Characterization of parameters with a mixed bias property | 1.000 | 7 | 3 | 100% |
| 7 | James Robins, Eric Tchetgen Tchetgen, Lingling Li, and Aad van der V… (2009) Semiparametric minimax rates | 0.928 | 4 | 3 | 100% |
| 8 | James M Robins, Lingling Li, Lin Liu, Rajarshi Mukherjee, Eric Tchet… (2017) Minimax estimation of a functional on a structured high-dimensional model self | 0.874 | 8 | 2 | 100% |
| 9 | Matteo Bonvini and Edward H Kennedy (2022) Fast convergence rates for dose-response estimation | 0.737 | 3 | 2 | 100% |
| 10 | Edward H Kennedy, Sivaraman Balakrishnan, and Larry Wasserman (2022) Minimax rates for heterogeneous causal effect estimation | 0.737 | 3 | 2 | 100% |
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