# New √n-consistent, numerically stable higher-order influence function estimators

arXiv: https://arxiv.org/abs/2302.08097 · HTML: https://mlsanity.com/paper/2302.08097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 10 of 10)

- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Augmented Minimax Linear Estimation](https://mlsanity.com/paper/1712.00038/) (2017)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [DeepMed: Semiparametric Causal Mediation Analysis with Debiased Deep Learning](https://mlsanity.com/paper/2210.04389/) (2022)
- [Higher Order Tangent Spaces and Influence Functions](https://mlsanity.com/paper/1502.00812/) (2015)
- [Fast convergence rates for dose-response estimation](https://mlsanity.com/paper/2207.11825/) (2022)
- [Rejoinder: On nearly assumption-free tests of nominal confidence interval coverage for causal parameters estimated by machine learning](https://mlsanity.com/paper/2008.03288/) (2020)
- [Causal Inference of General Treatment Effects using Neural Networks with A Diverging Number of Confounders](https://mlsanity.com/paper/2009.07055/) (2020)
- [Treatment Effects Estimation by Uniform Transformer](https://mlsanity.com/paper/2008.03738/) (2020)

## Built on by (most cited first, 1 of 1)

- [Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms](https://mlsanity.com/paper/2607.04743/) (2026)

## Abstract (arXiv)

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).