A Large Sample Study of Fuzzy Least-Squares Estimation
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...
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MDPI AG
2025-02-01
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| author | Jin Hee Yoon Seung Hoe Choi |
| author_facet | Jin Hee Yoon Seung Hoe Choi |
| author_sort | Jin Hee Yoon |
| collection | DOAJ |
| description | 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–output 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. |
| format | Article |
| id | doaj-art-4258ec3b9d8142cbbf3586874624e8f6 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-4258ec3b9d8142cbbf3586874624e8f62025-08-20T02:42:45ZengMDPI AGAxioms2075-16802025-02-0114318110.3390/axioms14030181A Large Sample Study of Fuzzy Least-Squares EstimationJin Hee Yoon0Seung Hoe Choi1Department of Mathematics and Statistics, Sejong University, Seoul 05006, Republic of KoreaSchool of Liberal Arts and Science, Korea Aerospace University, Goyang 10540, Republic of KoreaIn 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–output 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.https://www.mdpi.com/2075-1680/14/3/181fuzzy least-squares estimationasymptotic normalitystrong consistencytriangular fuzzy matrix |
| spellingShingle | Jin Hee Yoon Seung Hoe Choi A Large Sample Study of Fuzzy Least-Squares Estimation Axioms fuzzy least-squares estimation asymptotic normality strong consistency triangular fuzzy matrix |
| title | A Large Sample Study of Fuzzy Least-Squares Estimation |
| title_full | A Large Sample Study of Fuzzy Least-Squares Estimation |
| title_fullStr | A Large Sample Study of Fuzzy Least-Squares Estimation |
| title_full_unstemmed | A Large Sample Study of Fuzzy Least-Squares Estimation |
| title_short | A Large Sample Study of Fuzzy Least-Squares Estimation |
| title_sort | large sample study of fuzzy least squares estimation |
| topic | fuzzy least-squares estimation asymptotic normality strong consistency triangular fuzzy matrix |
| url | https://www.mdpi.com/2075-1680/14/3/181 |
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