# Higher Order Tangent Spaces and Influence Functions

arXiv: https://arxiv.org/abs/1502.00812 · HTML: https://mlsanity.com/paper/1502.00812/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2015.

## Built on by (most cited first, 9 of 9)

- [The Fundamental Limits of Structure-Agnostic Functional Estimation](https://mlsanity.com/paper/2305.04116/) (2023)
- [Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation](https://mlsanity.com/paper/2402.14264/) (2024)
- [A Free Lunch with Influence Functions? Improving Neural Network Estimates with Concepts from Semiparametric Statistics](https://mlsanity.com/paper/2202.09096/) (2022)
- [Automated Efficient Estimation using Monte Carlo Efficient Influence Functions](https://mlsanity.com/paper/2403.00158/) (2024)
- [Robust Causal Learning for the Estimation of Average Treatment Effects](https://mlsanity.com/paper/2209.01805/) (2022)
- [Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators](https://mlsanity.com/paper/2306.10590/) (2023)
- [New √n-consistent, numerically stable higher-order influence function estimators](https://mlsanity.com/paper/2302.08097/) (2023)
- [Robust Orthogonal Machine Learning of Treatment Effects](https://mlsanity.com/paper/2103.11869/) (2021)
- [Toward an Asymptotic Efficiency Theory on Regular Parameter Manifolds](https://mlsanity.com/paper/2510.13703/) (2025)

## Abstract (arXiv)

We review higher order tangent spaces and influence functions and their use to construct minimax efficient estimators for parameters in high-dimensional semiparametric models.