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Constrained center and range joint model for interval-valued symbolic data regression

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  • Hao, Peng
  • Guo, Junpeng

Abstract

A constrained center and range joint model to fit linear regression to interval-valued symbolic data is introduced. This new method applies both the center and range of the interval to fit a linear regression model, and avoids the negative value of the range of the predicted dependent interval variable by adding nonnegative constraints. To improve prediction accuracy it adopts overlapping constraints. Using a little algebra, it is constructed as a special case of the least squares with inequality (LSI) problem and is solved with a Matlab routine. The assessment of the proposed prediction method is based on an estimation of the average root mean square error and accuracy rate. In the framework of a Monte Carlo experiment, different data set configurations take into account the rich or lack of error, as well as the slope with respect to the dependent and independent variables. A statistical t-test compares the performance of the new model with that of four previously reported methods. Based on experiment results, it is outlined that the new model has better fitness. An analysis of outliers is performed to determine the effects of outliers on our proposal. The proposed method is illustrated by analyses of data from two real-life case studies to compare its performance with those of the other methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:116:y:2017:i:c:p:106-138
    DOI: 10.1016/j.csda.2017.06.005
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Hojati, Mehran & Bector, C. R. & Smimou, Kamal, 2005. "A simple method for computation of fuzzy linear regression," European Journal of Operational Research, Elsevier, vol. 166(1), pages 172-184, October.
    4. 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.
    5. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    6. Tao Xiong & Yukun Bao & Zhongyi Hu, 2014. "Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting," Papers 1401.1916, arXiv.org.
    7. 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.
    8. 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.
    9. Tanaka, Hideo & Hayashi, Isao & Watada, Junzo, 1989. "Possibilistic linear regression analysis for fuzzy data," European Journal of Operational Research, Elsevier, vol. 40(3), pages 389-396, June.
    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.
    11. 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.
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    Cited by:

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    2. Wagner J. F. Silva & Renata M. C. R. Souza & F. J. A. Cysneiros, 2022. "Bivariate elliptical regression for modeling interval-valued data," Computational Statistics, Springer, vol. 37(4), pages 2003-2028, September.
    3. Qing Zhao & Huiwen Wang & Shanshan Wang, 2023. "Robust regression for interval-valued data based on midpoints and log-ranges," 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. 17(3), pages 583-621, September.

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