# Semi-parametric efficiency bounds for high-dimensional models

arXiv: https://arxiv.org/abs/1601.00815 · HTML: https://mlsanity.com/paper/1601.00815/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2016.

## Built on by (most cited first, 5 of 5)

- [Debiased Machine Learning without Sample-Splitting for Stable Estimators](https://mlsanity.com/paper/2206.01825/) (2022)
- [Inference on Optimal Dynamic Policies via Softmax Approximation](https://mlsanity.com/paper/2303.04416/) (2023)
- [CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression](https://mlsanity.com/paper/2310.16819/) (2023)
- [Debiased Regression for Root-N-Consistent Conditional Mean Estimation](https://mlsanity.com/paper/2411.11748/) (2024)
- [Debiased Nonparametric Regression for Statistical Inference and Distributionally Robustness](https://mlsanity.com/paper/2412.20173/) (2024)

## Abstract (arXiv)

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models, where the dimension of the parameter is larger than the sample size. We adopt a semi-parametric point of view: we concentrate on one dimensional functions of a high-dimensional parameter. We follow two different approaches to reach the lower bounds: asymptotic Cram'er-Rao bounds and Le Cam's type of analysis. Both these approaches allow us to define a class of asymptotically unbiased or "regular" estimators for which a lower bound is derived. Consequently, we show that certain estimators obtained by de-sparsifying (or de-biasing) an ℓ1-penalized M-estimator are asymptotically unbiased and achieve the lower bound on the variance: thus in this sense they are asymptotically efficient. The paper discusses in detail the linear regression model and the Gaussian graphical model.