IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i9p2010-2029.html
   My bibliography  Save this article

Regression model for interval-valued variables based on copulas

Author

Listed:
  • Eufr�sio de A. Lima Neto
  • Ulisses U. dos Anjos

Abstract

In real problems, it is usual to have the available data presented as intervals. Therefore, different approaches have been proposed to obtain a regression model for this new type of data. In this paper, we represent the interval-valued response variable as a bivariate random vector and we consider the copula's theory to propose a general bivariate distribution for Z , creating a more flexible random component to the model. Inference techniques and a residual definition based on deviance are considered, as well as applications to synthetic and real data sets that demonstrate the usefulness of the proposed approach. The new method is also compared with other methods reported in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:9:p:2010-2029
    DOI: 10.1080/02664763.2015.1015114
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2015.1015114
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2015.1015114?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. Blanco-Fernández, Angela & Corral, Norberto & González-Rodríguez, Gil, 2011. "Estimation of a flexible simple linear model for interval data based on set arithmetic," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2568-2578, September.
    2. Billard L. & Diday E., 2003. "From the Statistics of Data to the Statistics of Knowledge: Symbolic Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 470-487, January.
    3. Lima Neto, Eufrasio de A. & de Carvalho, Francisco de A.T., 2008. "Centre and Range method for fitting a linear regression model to symbolic interval data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1500-1515, January.
    4. 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.
    5. Lima Neto, Eufrásio de A. & de Carvalho, Francisco de A.T., 2010. "Constrained linear regression models for symbolic interval-valued variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 333-347, February.
    6. Paula Brito & A. Pedro Duarte Silva, 2012. "Modelling interval data with Normal and Skew-Normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 3-20, March.
    7. Gil, Maria Angeles & Gonzalez-Rodriguez, Gil & Colubi, Ana & Montenegro, Manuel, 2007. "Testing linear independence in linear models with interval-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3002-3015, March.
    8. Groenen, P.J.F. & Winsberg, S. & Rodriguez, O. & Diday, E., 2006. "I-Scal: Multidimensional scaling of interval dissimilarities," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 360-378, November.
    9. Masakazu Iwasaki & Hiroe Tsubaki, 2005. "A new bivariate distribution in natural exponential family," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 323-336, June.
    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. Marta García-Bárzana & Ana Belén Ramos-Guajardo & Ana Colubi & Erricos J. Kontoghiorghes, 2020. "Multiple linear regression models for random intervals: a set arithmetic approach," Computational Statistics, Springer, vol. 35(2), pages 755-773, June.

    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. Yan Sun & Guanghua Lian & Zudi Lu & Jennifer Loveland & Isaac Blackhurst, 2020. "Modeling the Variance of Return Intervals Toward Volatility Prediction," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 492-519, July.
    2. Paolo Giordani, 2015. "Lasso-constrained regression analysis for interval-valued data," 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. 9(1), pages 5-19, March.
    3. Sun, Yuying & Zhang, Xinyu & Wan, Alan T.K. & Wang, Shouyang, 2022. "Model averaging for interval-valued data," European Journal of Operational Research, Elsevier, vol. 301(2), pages 772-784.
    4. Maia, André Luis Santiago & de Carvalho, Francisco de A.T., 2011. "Holt’s exponential smoothing and neural network models for forecasting interval-valued time series," International Journal of Forecasting, Elsevier, vol. 27(3), pages 740-759.
    5. Karel Hron & Paula Brito & Peter Filzmoser, 2017. "Exploratory data analysis for interval compositional data," 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(2), pages 223-241, June.
    6. Cheolwoo Park & Yongho Jeon & Kee-Hoon Kang, 2016. "An exploratory data analysis in scale-space for interval-valued data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2643-2660, October.
    7. Dias, Sónia & Brito, Paula, 2017. "Off the beaten track: A new linear model for interval data," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1118-1130.
    8. A. Pedro Duarte Silva & Peter Filzmoser & Paula Brito, 2018. "Outlier detection in interval data," 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. 12(3), pages 785-822, September.
    9. Hao, Peng & Guo, Junpeng, 2017. "Constrained center and range joint model for interval-valued symbolic data regression," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 106-138.
    10. Maia, André Luis Santiago & de Carvalho, Francisco de A.T., 2011. "Holt's exponential smoothing and neural network models for forecasting interval-valued time series," International Journal of Forecasting, Elsevier, vol. 27(3), pages 740-759, July.
    11. 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.
    12. Wei Yang & Ai Han & Yongmiao Hong & Shouyang Wang, 2016. "Analysis of crisis impact on crude oil prices: a new approach with interval time series modelling," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1917-1928, December.
    13. Henning Fischer & Ángela Blanco‐FERNÁndez & Peter Winker, 2016. "Predicting Stock Return Volatility: Can We Benefit from Regression Models for Return Intervals?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 35(2), pages 113-146, March.
    14. Sun, Yuying & Han, Ai & Hong, Yongmiao & Wang, Shouyang, 2018. "Threshold autoregressive models for interval-valued time series data," Journal of Econometrics, Elsevier, vol. 206(2), pages 414-446.
    15. Lima Neto, Eufrásio de A. & de Carvalho, Francisco de A.T., 2010. "Constrained linear regression models for symbolic interval-valued variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 333-347, February.
    16. Blanco-Fernández, Angela & Corral, Norberto & González-Rodríguez, Gil, 2011. "Estimation of a flexible simple linear model for interval data based on set arithmetic," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2568-2578, September.
    17. A. Silva & Paula Brito, 2015. "Discriminant Analysis of Interval Data: An Assessment of Parametric and Distance-Based Approaches," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 516-541, October.
    18. Lin, Wei & González-Rivera, Gloria, 2016. "Interval-valued time series models: Estimation based on order statistics exploring the Agriculture Marketing Service data," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 694-711.
    19. Antonio Calcagnì & Luigi Lombardi & Lorenzo Avanzi & Eduardo Pascali, 2020. "Multiple mediation analysis for interval-valued data," Statistical Papers, Springer, vol. 61(1), pages 347-369, February.
    20. Chang, Meng-Shiuh & Ju, Peijie & Liu, Yilei & Hsueh, Shao-Chieh, 2022. "Determining hedges and safe havens for stocks using interval analysis," The North American Journal of Economics and Finance, Elsevier, vol. 61(C).

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:42:y:2015:i:9:p:2010-2029. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.