IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v71y2013i3p279-306.html
   My bibliography  Save this article

Weighted Least Squares and Least Median Squares estimation for the fuzzy linear regression analysis

Author

Listed:
  • Pierpaolo D’Urso
  • Riccardo Massari

Abstract

In this paper, we discuss the problem of regression analysis in a fuzzy domain. By considering an iterative Weighted Least Squares estimation approach, we propose a general linear regression model for studying the dependence of a general class of fuzzy response variable, i.e., $$LR_2$$ L R 2 fuzzy variable or trapezoidal fuzzy variable,on a set of crisp or $$LR_2$$ L R 2 fuzzy explanatory variables. We also show some theoretical properties and a suitable generalization of the determination coefficient in order to investigate the goodness of fit of the regression model. Furthermore, we discuss some theoretical issues and an assessment of imprecision of the regression function. Finally, we suggest a robust version of the fuzzy regression model based on the Least Median Squares estimation approach which is able to neutralize and/or smooth the disruptive effects of possible crisp or fuzzy outliers in the estimation process. A simulation study and two empirical applications are presented. Copyright Sapienza Università di Roma 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:71:y:2013:i:3:p:279-306
    DOI: 10.1007/s40300-013-0025-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40300-013-0025-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s40300-013-0025-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Kim, Kwang Jae & Moskowitz, Herbert & Koksalan, Murat, 1996. "Fuzzy versus statistical linear regression," European Journal of Operational Research, Elsevier, vol. 92(2), pages 417-434, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Zhou, Jian & Shen, Yixuan & Pantelous, Athanasios A. & Zhang, Hui, 2021. "The range of uncertainty on the property market pricing: The case of the city of Shanghai," Finance Research Letters, Elsevier, vol. 40(C).

    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. 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.
    2. 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.
    3. Pavel Škrabánek & Jaroslav Marek & Alena Pozdílková, 2021. "Boscovich Fuzzy Regression Line," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    4. 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.
    5. 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.
    6. 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.
    7. Roldán López de Hierro, Antonio Francisco & Martínez-Moreno, Juan & Aguilar Peña, Concepción & Roldán López de Hierro, Concepción, 2016. "A fuzzy regression approach using Bernstein polynomials for the spreads: Computational aspects and applications to economic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 128(C), pages 13-25.
    8. 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.
    9. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    10. Maria Ferraro & Paolo Giordani, 2012. "A multiple linear regression model for imprecise information," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1049-1068, November.
    11. Koissi, Marie-Claire & Shapiro, Arnold F., 2006. "Fuzzy formulation of the Lee-Carter model for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 287-309, December.
    12. K. Smimou, 2013. "On the significance testing of fuzzy regression applied to the CAPM: Canadian commodity futures evidence," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 5(2), pages 144-171.
    13. F-M Tseng, 2008. "Quadratic interval innovation diffusion models for new product sales forecasting," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1120-1127, August.
    14. Carmen Nadia Ciocoiu & Adina Liliana Prioteasa & Sofia Elena Colesca, 2020. "Risk Management Implementation for Sustainable Development of Romanian SMEs: A Fuzzy Approach ...........," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 22(55), pages 726-726, August.
    15. R Fildes & K Nikolopoulos & S F Crone & A A Syntetos, 2008. "Forecasting and operational research: a review," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1150-1172, September.
    16. 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.
    17. Maryam Al-Kandari & Kingsley Adjenughwure & Kyriakos Papadopoulos, 2020. "A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models," Mathematics, MDPI, vol. 8(9), pages 1-10, August.
    18. Guo, Peijun & Tanaka, Hideo, 2006. "Dual models for possibilistic regression analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 253-266, November.
    19. 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.
    20. 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).

    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:spr:metron:v:71:y:2013:i:3:p:279-306. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.