Xingyu Chen, Lin Liu, Rajarshi Mukherjee
arXiv 12 Aug 2024 · Mathematics — Statistics Theory
arXiv:2408.06103 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider the estimation of regression coefficients and signal-to-noise (SNR) ratio in high-dimensional Generalized Linear Models (GLMs), and explore their implications in inferring popular estimands such as average treatment effects in high-dimensional observational studies. Under the “proportional asymptotic” regime and Gaussian covariates with known (population) covariance $\Sigma$, we derive Consistent and Asymptotically Normal (CAN) estimators of our targets of inference through a Method-of-Moments type of estimators that bypasses estimation of high dimensional nuisance functions and hyperparameter tuning altogether. Additionally, under non-Gaussian covariates, we demonstrate universality of our results under certain additional assumptions on the regression coefficients and $\Sigma$. We also demonstrate that knowing $\Sigma$ is not essential to our proposed methodology when the sample covariance matrix estimator is invertible. Finally, we complement our theoretical results with numerical experiments and comparisons with existing literature.
appendix boundary found by appendix_command · 47% of the source is main text. Read the extracted text to check this.
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 | Michael Celentano and Martin J Wainwright (2023) Challenges of the inconsistency regime: Novel debiasing methods for missing data models | 0.953 | 15 | 5 | 87% |
| 2 | Pierre C Bellec (2025) Observable adjustments in single-index models for regularized $M$-estimators with bounded $p / n$ | 0.941 | 12 | 4 | 83% |
| 3 | Weihao Kong and Gregory Valiant (2018) Estimating learnability in the sublinear data regime | 0.928 | 5 | 3 | 80% |
| 4 | Kazuma Sawaya, Yoshimasa Uematsu, and Masaaki Imaizumi (2023) Moment-based adjustments of statistical inference in high-dimensional generalized linear models | 0.874 | 8 | 2 | 100% |
| 5 | Lin Liu, Rajarshi Mukherjee, and James M Robins (2024) Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators self | 0.843 | 4 | 3 | 75% |
| 6 | Pragya Sur and Emmanuel J Candès (2019) A modern maximum-likelihood theory for high-dimensional logistic regression | 0.811 | 4 | 2 | 100% |
| 7 | Xiao Guo and Guang Cheng (2022) Moderate-dimensional inferences on quadratic functionals in ordinary least squares | 0.737 | 3 | 3 | 67% |
| 8 | Kuanhao Jiang, Rajarshi Mukherjee, Subhabrata Sen, and Pragya Sur (2025) A new central limit theorem for the augmented IPW estimator: Variance inflation, cross-fit covariance and beyond self | 0.737 | 3 | 2 | 100% |
| 9 | Yufan Li and Pragya Sur (2023) Spectrum-aware adjustment: A new debiasing framework with applications to principal components regression | 0.737 | 3 | 2 | 100% |
| 10 | James Robins, Lingling Li, Eric Tchetgen Tchetgen, and Aad van der V… (2008) Higher order influence functions and minimax estimation of nonlinear functionals | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 94 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Higher-Order Debiased Estimators for General Treatment Models | 0.644 | 2 | 2 |
| 2 | Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms | 0.644 | 2 | 2 |