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Articles

An adapted linear modeling method for interval-valued responses: Golden center and range method

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References

  • Billard, L., and E. Diday. 2000. “Regression Analysis for Interval-Valued Data.” In Data Analysis, Classification, and Related Methods, edited by H. A. L. Kiers, J.-P. Rasson, P. J. F. Groenen, and M. Schader, 369–374. Berlin: Springer.
  • Billard, L., and E. Diday. 2002. “Symbolic Regression Analysis. In: Classification, Clustering and Data Analysis.” In Proceedings of the Eighenth Conference of the International Federation of Classification Societies (IFCS’02), Springer. Poland, 281–288.
  • Box, G. E. P., and N. R. Draper. 2007. Response Surface Mixtures and Ridge Analysis.” Hoboken, NJ: Wiley.
  • Chacón, J. E., and O. Rodríguez. 2021. “Regression Models for Symbolic Interval-Valued Variables.” Entropy 23 (4):429. doi: 10.3390/e23040429.
  • Domingues, M. A., R. M. De Souza, and F. J. A. A. Cysneiros. 2010. “Robust Method for Linear Regression of Symbolic Interval Data.” Pattern Recognition Letters 31 (13):1991–1996. doi: 10.1016/j.patrec.2010.06.008.
  • Dunlap, R. A. 1997. The Golden Ratio and Fibonacci Numbers. Singapore: World Scientific Publishing.
  • Fagundes, R. A., R. M. De Souza, and F. J. A. Cysneiros. 2013. “Robust Regression with Application to Symbolic Interval Data.” Engineering Applications of Artificial Intelligence 26 (1):564–573. doi: 10.1016/j.engappai.2012.05.004.
  • Giordani, P. 2015. “Lasso-Constrained Regression Analysis for Interval-Valued Data.” Advances in Data Analysis and Classification 9 (1):5–19. doi: 10.1007/s11634-014-0164-8.
  • Harper, D., M. Kosbe, and L. Peyton. 1987. “Optimization of Ford Taurus Wheel Cover Balance (by Design of experiments-Taguchi’s Method).” Fifth Symposium on Taguchi Methods, Romulus, MI: American Supplier Institute, 527–539.
  • Lim, C. 2016. “Interval-Valued Data Regression Using Nonparametric Additive Models.” Journal of the Korean Statistical Society 45 (3):358–370. doi: 10.1016/j.jkss.2015.12.003.
  • Martens, H. A., and P. Dardenne. 1998. “Validation and Verification of Regression in Small Data Sets.” Chemometrics and Intelligent Laboratory Systems 44 (1–2):99–121. doi: 10.1016/S0169-7439(98)00167-1.
  • Montogomery, D., and B. Peck. 1981. Introduction to Linear Regression Analysis. New York: Wiley.
  • Neto, E. D. A. L., G. M. Cordeiro, and F. D. A. De Carvalho. 2011. “Bivariate Symbolic Regression Models for Interval-Valued Variables.” Journal of Statistical Computation and Simulation 81 (11):1727–1744. doi: 10.1080/00949655.2010.500470.
  • Neto, E. D. A. L., and F. D. A. De Carvalho. 2008. “Centre and Range Method for Fitting a Linear Regression Model to Symbolic Interval Data.” Computational Statistics & Data Analysis 52 (3):1500–1515. doi: 10.1016/j.csda.2007.04.014.
  • Neto, E. D. A. L., and F. D. A. De Carvalho. 2010. “Constrained Linear Regression Models for Symbolic Interval-Valued Variables.” Computational Statistics & Data Analysis 54 (2):333–347. doi: 10.1016/j.csda.2009.08.010.
  • Neto, E. D. A. L., and F. D. A. De Carvalho. 2018. “An Exponential-Type Kernel Robust Regression Model for Interval-Valued Variables.” Information Sciences 454–455:419–442. doi: 10.1016/j.ins.2018.05.008.
  • Souza, L. C., R. M. Souza, G. J. Amaral, and T. M. Silva Filho. 2017. “A Parametrized Approach for Linear Regression of Interval Data.” Knowledge-Based Systems 131:149–159. doi: 10.1016/j.knosys.2017.06.012.
  • Türkşen, Ö. 2016. “Analysis of Response Surface Model Parameters with Bayesian Approach and Fuzzy Approach.” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 24 (01):109–122. doi: 10.1142/S0218488516500069.
  • Vabalas, A., E. Gowen, E. Poliakoff, and A. J. Casson. 2019. “Machine Learning Algorithm Validation with a Limited Sample Size.” PloS One 14 (11):e0224365. doi: 10.1371/journal.pone.0224365.
  • Vorobiev, N. N. 2002. Fibonacci Numbers. Basel: Springer.
  • Vural, N., Ö. Algan Cavuldak, and R. E. Anl i. 2018. “Multi Response Optimisation of Polyphenol Extraction Conditions from Grape Seeds by Using Ultrasound Assisted Extraction (UAE).” Separation Science and Technology 53 (10):1540–1551. doi: 10.1080/01496395.2018.1442864.
  • Wang, H., R. Guan, and J. Wu. 2012. “Linear Regression of Interval-Valued Data Based on Complete Information in Hypercubes.” Journal of Systems Science and Systems Engineering 21 (4):422–442. doi: 10.1007/s11518-012-5203-4.
  • Xu, Y., and R. Goodacre. 2018. “On Splitting Training and Validation Set: A Comparative Study of Cross-Validation, Bootstrap and Systematic Sampling for Estimating the Generalization Performance of Supervised Learning.” Journal of Analysis and Testing 2 (3):249–262. doi: 10.1007/s41664-018-0068-2.
  • Xu, W. 2010. “Symbolic Data Analysis: interval-Valued Data Regression.” Doctoral dissertation., University of Georgia.

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