IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i2p333-347.html
   My bibliography  Save this article

Constrained linear regression models for symbolic interval-valued variables

Author

Listed:
  • Lima Neto, Eufrásio de A.
  • de Carvalho, Francisco de A.T.

Abstract

This paper introduces an approach to fitting a constrained linear regression model to interval-valued data. Each example of the learning set is described by a feature vector for which each feature value is an interval. The new approach fits a constrained linear regression model on the midpoints and range of the interval values assumed by the variables in the learning set. The prediction of the lower and upper boundaries of the interval value of the dependent variable is accomplished from its midpoint and range, which are estimated from the fitted linear regression models applied to the midpoint and range of each interval value of the independent variables. This new method shows the importance of range information in prediction performance as well as the use of inequality constraints to ensure mathematical coherence between the predicted values of the lower () and upper () boundaries of the interval. The authors also propose an expression for the goodness-of-fit measure denominated determination coefficient. The assessment of the proposed prediction method is based on the estimation of the average behavior of the root-mean-square error and square of the correlation coefficient in the framework of a Monte Carlo experiment with different data set configurations. Among other aspects, the synthetic data sets take into account the dependence, or lack thereof, between the midpoint and range of the intervals. The bias produced by the use of inequality constraints over the vector of parameters is also examined in terms of the mean-square error of the parameter estimates. Finally, the approaches proposed in this paper are applied to a real data set and performances are compared.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:333-347
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00306-5
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Dorfman, Jeffrey H. & McIntosh, Christopher S., 2001. "Imposing inequality restrictions: efficiency gains from economic theory," Economics Letters, Elsevier, vol. 71(2), pages 205-209, May.
    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. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Fei Liu & L. Billard, 2022. "Partition of Interval-Valued Observations Using Regression," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 55-77, March.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Carlo Drago & Roberto Ricciuti, 2019. "An interval variables approach to address measurement uncertainty in governance indicators," Economics Bulletin, AccessEcon, vol. 39(1), pages 626-635.
    17. 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).
    18. 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.
    19. Liang-Ching Lin & Hsiang-Lin Chien & Sangyeol Lee, 2021. "Symbolic interval-valued data analysis for time series based on auto-interval-regressive models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 295-315, March.
    20. Gloria Gonzalez-Rivera & Javier Arroyo & Carlos Mate, 2011. "Forecasting with Interval and Histogram Data. Some Financial Applications," Working Papers 201438, University of California at Riverside, Department of Economics.

    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:eee:csdana:v:54:y:2010:i:2:p:333-347. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.