IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p1956-d440138.html
   My bibliography  Save this article

On Optimal and Asymptotic Properties of a Fuzzy L 2 Estimator

Author

Listed:
  • Jin Hee Yoon

    (Department of Mathematics and Statistics, Sejong University, Seoul 05006, Korea)

  • Przemyslaw Grzegorzewski

    (Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Wasaw, Poland
    Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland)

Abstract

A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L 2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

Suggested Citation

  • Jin Hee Yoon & Przemyslaw Grzegorzewski, 2020. "On Optimal and Asymptotic Properties of a Fuzzy L 2 Estimator," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1956-:d:440138
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/1956/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/1956/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. D'Urso, Pierpaolo & Gastaldi, Tommaso, 2000. "A least-squares approach to fuzzy linear regression analysis," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 427-440, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Coppi, Renato & D'Urso, Pierpaolo & Giordani, Paolo & Santoro, Adriana, 2006. "Least squares estimation of a linear regression model with LR fuzzy response," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 267-286, November.
    2. D'Urso, Pierpaolo & Giordani, Paolo, 2003. "A least squares approach to Principal Component Analysis for interval valued data," Economics & Statistics Discussion Papers esdp03013, University of Molise, Department of Economics.
    3. Pierpaolo D’Urso & Marta Disegna & Riccardo Massari, 2020. "Satisfaction and Tourism Expenditure Behaviour," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(3), pages 1081-1106, June.
    4. Giordani, Paolo & Kiers, Henk A. L., 2004. "Principal Component Analysis of symmetric fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 519-548, April.
    5. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    6. Belhadj, Besma, 2023. "New fuzzy multiple regressions for the instantaneous and panel data “The determinants of Poverty in the Countries MENA”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    7. Enrico Ciavolino & Antonio Calcagnì, 2014. "A generalized maximum entropy (GME) approach for crisp-input/fuzzy-output regression model," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3401-3414, November.
    8. A. Blanco-Fernández & A. Ramos-Guajardo & A. Colubi, 2013. "Fuzzy representations of real-valued random variables: applications to exploratory and inferential studies," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 245-259, November.
    9. D'Urso, Pierpaolo, 2003. "Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 47-72, February.
    10. Pavel Škrabánek & Jaroslav Marek & Alena Pozdílková, 2021. "Boscovich Fuzzy Regression Line," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    11. Wu, Hsien-Chung, 2003. "Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 203-217, February.
    12. Pierpaolo D’Urso & Riccardo Massari, 2013. "Weighted Least Squares and Least Median Squares estimation for the fuzzy linear regression analysis," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 279-306, November.
    13. Pierpaolo D’Urso & María Ángeles Gil, 2017. "Fuzzy data analysis and classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 645-657, December.
    14. Antonio Terceño & María Glòria Barberà-Mariné & Yanina Laumann, 2018. "Análisis de los coeficientes beta: evidencia en el mercado de activos chileno," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 21(3), pages 076-093, December.
    15. Belhadj, Besma, 2024. "Fuzzy multiple regressions for Cross-Section and Panel data," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).
    16. Eufr�sio de A. Lima Neto & Ulisses U. dos Anjos, 2015. "Regression model for interval-valued variables based on copulas," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(9), pages 2010-2029, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1956-:d:440138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.