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Bivariate elliptical regression for modeling interval-valued data

Author

Listed:
  • Wagner J. F. Silva

    (Universidade Federal de Pernambuco)

  • Renata M. C. R. Souza

    (Universidade Federal de Pernambuco)

  • F. J. A. Cysneiros

    (Universidade Federal de Pernambuco)

Abstract

This paper introduces a special case of a multivariate regression model with restriction for interval-valued data in the symbolic data analysis framework. This model is less sensitive in the presence of interval outliers since it considers light-heavy tails distributions. Intervals are obtained from classic data according to a fusion process and each interval can be represented by its center and range data or lower and upper bound values. The correlation between the center and range variables or lower and upper bound variables is a fundamental component for constructing the model. Therefore, a study that provides a suitable choice of the representation for intervals in bivariate models is proposed. Simulation studies in the Monte Carlo framework regarding different scenarios of interval data set with and without outliers are carried out to validate the proposed model. An application with real-life interval medical dataset is also performed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01189-x
    DOI: 10.1007/s00180-021-01189-x
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    References listed on IDEAS

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    1. Kibria, B. M. Golam & Haq, M. Safiul, 1999. "Predictive Inference for the Elliptical Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 235-249, February.
    2. 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.
    3. 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.
    4. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    5. 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.
    6. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
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