IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p1000-d373382.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/1000/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/1000/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hao Zhang & Dale L. Zimmerman, 2005. "Towards reconciling two asymptotic frameworks in spatial statistics," Biometrika, Biometrika Trust, vol. 92(4), pages 921-936, December.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Bhatti, Chad R., 2010. "The Birnbaum–Saunders autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2062-2078.
    9. 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.
    10. 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.
    11. 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.
    12. Daniel P. McMillen, 2013. "Quantile Regression for Spatial Data," SpringerBriefs in Regional Science, Springer, edition 127, number 978-3-642-31815-3, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    4. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Víctor Leiva & Helton Saulo & Rubens Souza & Robert G. Aykroyd & Roberto Vila, 2021. "A new BISARMA time series model for forecasting mortality using weather and particulate matter data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 346-364, March.
    2. Saulo, Helton & Balakrishnan, Narayanaswamy & Vila, Roberto, 2023. "On a quantile autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 425-448.
    3. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    4. Helton Saulo & Narayanaswamy Balakrishnan & Roberto Vila, 2021. "On a quantile autoregressive conditional duration model applied to high-frequency financial data," Papers 2109.03844, arXiv.org.
    5. Hajime Seya & Kay W. Axhausen & Makoto Chikaraishi, 2020. "Spatial unconditional quantile regression: application to Japanese parking price data," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 65(2), pages 351-402, October.
    6. Danúbia R. Cunha & Roberto Vila & Helton Saulo & Rodrigo N. Fernandez, 2020. "A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data," JRFM, MDPI, vol. 13(3), pages 1-20, March.
    7. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    8. Luis Sánchez & Víctor Leiva & Helton Saulo & Carolina Marchant & José M. Sarabia, 2021. "A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications," Mathematics, MDPI, vol. 9(21), pages 1-21, November.
    9. Kakizawa, Yoshihide, 2022. "Multivariate elliptical-based Birnbaum–Saunders kernel density estimation for nonnegative data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    10. Haiyong Zhang & Xinyu Wang, 2018. "The impact of structural adjustment on housing prices in China," Asian-Pacific Economic Literature, The Crawford School, The Australian National University, vol. 32(1), pages 108-119, May.
    11. McMillen, Daniel, 2015. "Conditionally parametric quantile regression for spatial data: An analysis of land values in early nineteenth century Chicago," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 28-38.
    12. Bohman, Helena & Nilsson, Désirée, 2016. "The impact of regional commuter trains on property values: Price segments and income," Journal of Transport Geography, Elsevier, vol. 56(C), pages 102-109.
    13. Vilca, Filidor & Romeiro, Renata G. & Balakrishnan, N., 2016. "A bivariate Birnbaum–Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 169-183.
    14. Luc Anselin, 2019. "Quantile local spatial autocorrelation," Letters in Spatial and Resource Sciences, Springer, vol. 12(2), pages 155-166, August.
    15. Zhang, Lei & Leonard, Tammy, 2014. "Neighborhood impact of foreclosure: A quantile regression approach," Regional Science and Urban Economics, Elsevier, vol. 48(C), pages 133-143.
    16. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.
    17. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "The bivariate Sinh-Elliptical distribution with applications to Birnbaum–Saunders distribution and associated regression and measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 1-16.
    18. Zhu, Xiaojun & Balakrishnan, N., 2015. "Birnbaum–Saunders distribution based on Laplace kernel and some properties and inferential issues," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 1-10.
    19. McMillen, Daniel & Shimizu, Chihiro, 2017. "Decompositions of Spatially Varying Quantile Distribution Estimates: The Rise and Fall of Tokyo House Prices," HIT-REFINED Working Paper Series 74, Institute of Economic Research, Hitotsubashi University.
    20. Jochen Ranger & Jörg-Tobias Kuhn & José-Luis Gaviria, 2015. "A Race Model for Responses and Response Times in Tests," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 791-810, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1000-:d:373382. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.