Moment-Based Adjustments of Statistical Inference in High-Dimensional Generalized Linear Models

[2305.17731] Moment-Based Adjustments of Statistical Inference in High-Dimensional Generalized Linear Models Skip to main content Search Submit Donate Log in Mathematics > Statistics Theory arXiv:2305.17731 (math) [Submitted on 28 May 2023 ( v1 ), last revised 25 Aug 2026 (this version, v5)] Title: Moment-Based Adjustments of Statistical Inference in High-Dimensional Generalized Linear Models Authors: Kazuma Sawaya , Yoshimasa Uematsu , Masaaki Imaizumi View PDF HTML (experimental) Abstract: We develop a statistical inference method for generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients $p$ is of the same order as the sample size $n$. In this regime, constructing confidence intervals requires estimating unknown hyperparameters, such as the signal strength. However, existing estimators for the hyperparameters are not stably applicable to GLMs when $p/n$ is close to or greater than $1$, both theoretically and empirically. In this study, we develop an estimator for the hyperparameter that addresses the issue and establish an inferential framework, provided that the link function of the GLM exhibits an asymmetry property. The proposed estimator utilizes the moments of the output variable of GLMs and a convex surrogate loss. Our framework is theoretically valid even when the limit of $p/n$ exceeds $1$, ensuring the strong consistency of the hyperparameter estimator and asymptotically attaining the exact coverage probability of the confidence intervals. Our numerical experiments support these theoretical results. Comments: Accepted at Electric Journal of Statistics Subjects: Statistics Theory (math.ST) Cite as: arXiv:2305.17731 [math.ST] (or arXiv:2305.17731v5 [math.ST] for this version) https://doi.org/10.48550/arXiv.2305.17731 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Masaaki Imaizumi [ view email ] [v1] Sun, 28 May 2023 14:07:10 UTC (407 KB) [v2] Tue, 30 May 2023 02:43:31 UTC (407 KB) [v3] Wed, 25 Oct 2023 15:55:06 UTC (471 KB) [v4] Thu, 23 May 2024 11:13:26 UTC (1,478 KB) [v5] Tue, 25 Aug 2026 05:18:43 UTC (463 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2023-05 Change to browse by: math stat stat.TH References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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