{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T11:10:17Z","timestamp":1762081817893,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,31]],"date-time":"2022-12-31T00:00:00Z","timestamp":1672444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018615","name":"Key University Science Research Project of Jiangsu Province","doi-asserted-by":"publisher","award":["21KJB110023","91646106"],"award-info":[{"award-number":["21KJB110023","91646106"]}],"id":[{"id":"10.13039\/501100018615","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China","award":["21KJB110023","91646106"],"award-info":[{"award-number":["21KJB110023","91646106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The optimal subsampling is an statistical methodology for generalized linear models (GLMs) to make inference quickly about parameter estimation in massive data regression. Existing literature only considers bounded covariates. In this paper, the asymptotic normality of the subsampling M-estimator based on the Fisher information matrix is obtained. Then, we study the asymptotic properties of subsampling estimators of unbounded GLMs with nonnatural links, including conditional asymptotic properties and unconditional asymptotic properties.<\/jats:p>","DOI":"10.3390\/e25010084","type":"journal-article","created":{"date-parts":[[2023,1,2]],"date-time":"2023-01-02T04:51:22Z","timestamp":1672635082000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotics of Subsampling for Generalized Linear Regression Models under Unbounded Design"],"prefix":"10.3390","volume":"25","author":[{"given":"Guangqiang","family":"Teng","sequence":"first","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boping","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0825-6740","authenticated-orcid":false,"given":"Yuanyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Soochow University, Suzhou 215006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Industrial Systems Engineering & Management, National University of Singapore, 21 Lowr Kent Ridge Road, Singapore 119077, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.4310\/SII.2016.v9.n4.a4","article-title":"Direct regression modelling of high-order moments in big data","volume":"9","author":"Xi","year":"2016","journal-title":"Stat. 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