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Estimation of a flexible simple linear model for interval data based on set arithmetic

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  • Blanco-Fernández, Angela
  • Corral, Norberto
  • González-Rodríguez, Gil

Abstract

The estimation of a simple linear regression model when both the independent and dependent variable are interval valued is addressed. The regression model is defined by using the interval arithmetic, it considers the possibility of interval-valued disturbances, and it is less restrictive than existing models. After the theoretical formalization, the least-squares (LS) estimation of the linear model with respect to a suitable distance in the space of intervals is developed. The LS approach leads to a constrained minimization problem that is solved analytically. The strong consistency of the obtained estimators is proven. The estimation procedure is reinforced by a real-life application and some simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2568-2578
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    References listed on IDEAS

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    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. 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. Angela Blanco-Fernández & Peter Winker, 2016. "Data generation processes and statistical management of interval data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 475-494, October.
    5. 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.
    6. 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.
    7. 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.
    8. Wang, Xun & Zhang, Zhongzhan & Li, Shoumei, 2016. "Set-valued and interval-valued stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 208-223.
    9. Jian Li & Ping Qing & Wuyang Hu & Minglai Li, 2022. "Contract farming, community effect, and farmer valuation of biofortified crop varieties in China: The case of high‐zinc wheat," Review of Development Economics, Wiley Blackwell, vol. 26(2), pages 1035-1055, May.
    10. Wenhua Li & Junpeng Guo & Ying Chen & Minglu Wang, 2016. "A New Representation of Interval Symbolic Data and Its Application in Dynamic Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 149-165, April.
    11. 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.
    12. Ana Belén Ramos-Guajardo, 2022. "A hierarchical clustering method for random intervals based on a similarity measure," Computational Statistics, Springer, vol. 37(1), pages 229-261, March.
    13. 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.
    14. Henning Fischer & Marta García-Bárzana & Peter Tillmann & Peter Winker, 2014. "Evaluating FOMC forecast ranges: an interval data approach," Empirical Economics, Springer, vol. 47(1), pages 365-388, August.
    15. Yoichi Tsuchiya, 2021. "The value added of the Bank of Japan's range forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(5), pages 817-833, August.
    16. 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.
    17. 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.
    18. Ai Han & Yanan He & Yongmiao Hong & Shouyang Wang, 2013. "Forecasting Interval-valued Crude Oil Prices via Autoregressive Conditional Interval Models," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

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