{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/method-of-moments-inference-for-glms-and","title":"Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics","arxiv_id":"2408.06103","date":"2024-08-12","proceeding":null,"authors":["Xingyu Chen","Lin Liu","Rajarshi Mukherjee"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2408.06103v3","url_pdf":"https://arxiv.org/pdf/2408.06103v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"method-of-moments-inference-for-glms-and","repo_url":"https://github.com/cxy0714/method-of-moments-inference-for-glms","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}