Abstract
We study estimation of regression coefficients and the signal-to-noise ratio in high-dimensional generalized linear models, together with implications for inference on functionals such as average treatment effects in observational studies. Under proportional asymptotics and Gaussian covariates with known population covariance, we construct method-of-moments estimators that are consistent and asymptotically normal, without estimating high-dimensional nuisance functions or tuning hyperparameters. For non-Gaussian covariates, we establish universality under additional assumptions on the regression coefficients and covariance matrix. We also show how to proceed without known population covariance when the sample covariance estimator is invertible. Numerical experiments compare the proposed methods with existing approaches.
Links
🔗 arXiv 💻 Software 🖼 Poster 🎞 Slides
Xingyu Chen, Lin Liu, Rajarshi Mukherjee. Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics. arXiv preprint arXiv:2408.06103, 2024.