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Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data

Author

Listed:
  • Luis Sánchez

    (Department of Mathematics and Statistics, Universidad de La Frontera, Temuco 4780000, Chile)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Manuel Galea

    (Department of Statistics, Pontificia Universidad Católica de Chile, Santiago 8320000, Chile)

  • Helton Saulo

    (Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil)

Abstract

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.

Suggested Citation

  • Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2020. "Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1000-:d:373382
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    References listed on IDEAS

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    1. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    2. Víctor Leiva & Manoel Santos‐Neto & Francisco José A. Cysneiros & Michelli Barros, 2016. "A methodology for stochastic inventory models based on a zero‐adjusted Birnbaum‐Saunders distribution," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(1), pages 74-89, January.
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    4. Helton Saulo & Jeremias Leão & Roberto Vila & Victor Leiva & Vera Tomazella, 2020. "On mean-based bivariate Birnbaum-Saunders distributions: Properties, inference and application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(24), pages 6032-6056, December.
    5. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.
    6. Marcelo Ventura & Helton Saulo & Victor Leiva & Sandro Monsueto, 2019. "Log‐symmetric regression models: information criteria and application to movie business and industry data with economic implications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(4), pages 963-977, July.
    7. Carolina Marchant & Víctor Leiva & Francisco José A. Cysneiros & Juan F. Vivanco, 2016. "Diagnostics in multivariate generalized Birnbaum-Saunders regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2829-2849, November.
    8. Helton Saulo & Jeremias Leão & Víctor Leiva & Robert G. Aykroyd, 2019. "Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data," Statistical Papers, Springer, vol. 60(5), pages 1605-1629, October.
    9. Philip Kostov, 2009. "A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(1), pages 53-72.
    10. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, A., 2010. "Bivariate Birnbaum-Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 113-125, January.
    11. Daniel P. McMillen, 2013. "Quantile Regression for Spatial Data," SpringerBriefs in Regional Science, Springer, edition 127, number 978-3-642-31815-3.
    12. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
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    Cited by:

    1. Helton Saulo & Alan Dasilva & Víctor Leiva & Luis Sánchez & Hanns de la Fuente‐Mella, 2022. "Log‐symmetric quantile regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 124-163, May.
    2. Ramón Giraldo & Víctor Leiva & Cecilia Castro, 2023. "An Overview of Kriging and Cokriging Predictors for Functional Random Fields," Mathematics, MDPI, vol. 11(15), pages 1-22, August.
    3. Gabriela M. Rodrigues & Edwin M. M. Ortega & Gauss M. Cordeiro & Roberto Vila, 2023. "Quantile Regression with a New Exponentiated Odd Log-Logistic Weibull Distribution," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    4. Danilo Leal & Rodrigo Jiménez & Marco Riquelme & Víctor Leiva, 2023. "Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    5. Helton Saulo & Roberto Vila & Giovanna V. Borges & Marcelo Bourguignon & Víctor Leiva & Carolina Marchant, 2023. "Modeling Income Data via New Parametric Quantile Regressions: Formulation, Computational Statistics, and Application," Mathematics, MDPI, vol. 11(2), pages 1-25, January.

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