High-Dimensional Single-Index Models: Link Estimation and Marginal Inference

[2404.17812] High-Dimensional Single-Index Models: Link Estimation and Marginal Inference Skip to main content Search Submit Donate Log in Mathematics > Statistics Theory arXiv:2404.17812 (math) [Submitted on 27 Apr 2024 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: High-Dimensional Single-Index Models: Link Estimation and Marginal Inference Authors: Kazuma Sawaya , Yoshimasa Uematsu , Masaaki Imaizumi View PDF HTML (experimental) Abstract: This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable. Unlike previous approaches, which often overlook the estimation of the unknown link function, we introduce a new method for link function estimation. Leveraging the information from the estimated link function, we propose more efficient estimators that are better aligned with the underlying model. Furthermore, we rigorously establish the asymptotic normality of each coordinate of the estimator. This provides a valid construction of confidence intervals and $p$-values for any finite collection of coordinates. Numerical experiments validate our theoretical results. Comments: Accepted at Information and Inference: a journal of the IMA Subjects: Statistics Theory (math.ST) ; Methodology (stat.ME) Cite as: arXiv:2404.17812 [math.ST] (or arXiv:2404.17812v2 [math.ST] for this version) https://doi.org/10.48550/arXiv.2404.17812 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Masaaki Imaizumi [ view email ] [v1] Sat, 27 Apr 2024 07:33:32 UTC (287 KB) [v2] Tue, 25 Aug 2026 05:43:05 UTC (329 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2024-04 Change to browse by: math stat stat.ME stat.TH References & Citations NASA ADS 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) Major funding support from

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