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Lasso-constrained regression analysis for interval-valued data

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  • Paolo Giordani

Abstract

A new method of regression analysis for interval-valued data is proposed. The relationship between an interval-valued response variable and a set of interval-valued explanatory variables is investigated by considering two regression models, one for the midpoints and the other one for the radii. The estimation problem is approached by introducing Lasso-based constraints on the regression coefficients. This can improve the prediction accuracy of the model and, taking into account the nature of the constraints, can sometimes produce a parsimonious model with a common subset of regression coefficients for the midpoint and the radius models. The effectiveness of our method, called Lasso-IR (Lasso-based Interval-valued Regression), is shown by a simulation experiment and some applications to real data. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:9:y:2015:i:1:p:5-19
    DOI: 10.1007/s11634-014-0164-8
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    References listed on IDEAS

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    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. 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:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Wenyang Huang & Huiwen Wang & Shanshan Wang, 2021. "Dimension reduction of open-high-low-close data in candlestick chart based on pseudo-PCA," Papers 2103.16908, arXiv.org.

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