{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T01:24:18Z","timestamp":1772846658091,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T00:00:00Z","timestamp":1740700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT)","award":["RS-2024-00351610"],"award-info":[{"award-number":["RS-2024-00351610"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In many real-world situations, we deal with data that exhibit both randomness and vagueness. To manage such uncertain information, fuzzy theory provides a useful framework. Specifically, to explore causal relationships in these datasets, a lot of fuzzy regression models have been introduced. However, while fuzzy regression analysis focuses on estimation, it is equally important to study the mathematical characteristics of fuzzy regression estimates. Despite the statistical significance of optimal properties in large-sample scenarios, only limited research has addressed these topics. This study establishes key optimal properties, such as strong consistency and asymptotic normality, for the fuzzy least-squares estimator (FLSE) in general linear regression models involving fuzzy input\u2013output data and random errors. To achieve this, fuzzy analogues of traditional normal equations and FLSEs are derived using a suitable fuzzy metric. Additionally, a confidence region based on FLSEs is proposed to facilitate inference. The asymptotic relative efficiency of FLSEs, compared to conventional least-squares estimators, is also analyzed to highlight the efficiency of the proposed estimators.<\/jats:p>","DOI":"10.3390\/axioms14030181","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T10:46:46Z","timestamp":1740739606000},"page":"181","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Large Sample Study of Fuzzy Least-Squares Estimation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1437-1350","authenticated-orcid":false,"given":"Jin Hee","family":"Yoon","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Sejong University, Seoul 05006, Republic of Korea"}]},{"given":"Seung Hoe","family":"Choi","sequence":"additional","affiliation":[{"name":"School of Liberal Arts and Science, Korea Aerospace University, Goyang 10540, Republic of Korea"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.ins.2013.09.024","article-title":"A unified approach of asymptotic behaviors for the autoregressive model with fuzzy data","volume":"257","author":"Jung","year":"2014","journal-title":"Inform. 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