Least Squares Estimation For Hierarchical Data

[2404.13164] Least Squares Estimation For Hierarchical Data Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Computation arXiv:2404.13164 (stat) [Submitted on 19 Apr 2024 ( v1 ), last revised 1 May 2026 (this version, v3)] Title: Least Squares Estimation For Hierarchical Data Authors: Ryan Cumings-Menon , Pavel Zhuravlev View a PDF of the paper titled Least Squares Estimation For Hierarchical Data, by Ryan Cumings-Menon and 1 other authors View PDF HTML (experimental) Abstract: The U.S. Census Bureau's 2020 Disclosure Avoidance System (DAS) bases its output on noisy measurements, which are population tabulations added to realizations of mean-zero random variables. These noisy measurements are observed for a set of hierarchical geographic levels, e.g., the U.S. as a whole, states, counties, census tracts, and census blocks. The Census Bureau released the noisy measurements generated in the DAS executions for the two primary 2020 Census data products, in part to allow data users to assess uncertainty in 2020 Census tabulations introduced by disclosure avoidance. This paper describes an algorithm that can leverage the hierarchical structure of the input data in order to compute very high dimensional least squares estimates in a computationally efficient manner. Afterward, we show that this algorithm's output is equal to the generalized least squares estimator, describe how to find the variance of linear functions of this estimator, and provide a numerical experiment in which we compute confidence intervals of tabulations based on this estimator. We also describe an accompanying Census Bureau experimental data product that applies this estimator to the publicly available noisy measurements to provide data users with the inputs required to derive confidence intervals for all tabulations that were included in the 2020 Redistricting Data File, for the U.S., state, county, and census tract geographic levels. Subjects: Computation (stat.CO) ; Cryptography and Security (cs.CR) Cite as: arXiv:2404.13164 [stat.CO] (or arXiv:2404.13164v3 [stat.CO] for this version) https://doi.org/10.48550/arXiv.2404.13164 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ryan Cumings-Menon [ view email ] [v1] Fri, 19 Apr 2024 20:18:16 UTC (160 KB) [v2] Wed, 4 Jun 2025 12:13:43 UTC (312 KB) [v3] Fri, 1 May 2026 15:16:04 UTC (321 KB) Full-text links: Access Paper: View a PDF of the paper titled Least Squares Estimation For Hierarchical Data, by Ryan Cumings-Menon and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.CO < prev | next > new | recent | 2024-04 Change to browse by: cs cs.CR stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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

Related documents

• Least Squares Estimation For Hierarchical Data#189184
• Least Squares Estimation For Hierarchical Data#189084
• Least Squares Estimation For Hierarchical Data#189034
• Riemannian Regression#1154505
• Binning-Independent Bayesian Analysis of Time-Dependent Perturbed Angular Distribution data#1013826