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Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data

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  • Luis Sánchez
  • Víctor Leiva
  • Manuel Galea
  • Helton Saulo

Abstract

The Birnbaum‐Saunders (BS) distribution is a model that frequently appears in the statistical literature and has proved to be very versatile and efficient across a wide range of applications. However, despite the growing interest in the study of the BS distribution, quantile regression modeling has not been considered for this distribution. To fill this gap, we introduce a class of quantile regression models based on the BS distribution, which allows us to describe positive and asymmetric data when a quantile must be predicted using covariates. We use an approach based on a quantile parameterization to generate the model, permitting us to consider a similar framework to generalized linear models, providing wide flexibility. The methodology proposed includes a thorough study of theoretical properties and practical issues, such as maximum likelihood parameter estimation and diagnostic analytics based on local influence and residuals. The performance of the residuals is evaluated by simulations, whereas an illustrative example of income data is conducted using the methodology to show its potential for applications. The numerical results report an adequate performance of the approach to quantile regression, indicating that the BS distribution is a good modeling choice when dealing with data that have both positive support and asymmetry. The economic implications of our investigation are discussed in the final section. Hence, it can be a valuable addition to the tool kit of applied statisticians and econometricians.

Suggested Citation

  • Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2021. "Birnbaum‐Saunders quantile regression and its diagnostics with application to economic data," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 37(1), pages 53-73, January.
    • Handle: RePEc:wly:apsmbi:v:37:y:2021:i:1:p:53-73
    DOI: 10.1002/asmb.2556
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    References listed on IDEAS

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    1. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    2. Carolina Marchant & Víctor Leiva & George Christakos & M. Fernanda Cavieres, 2019. "Monitoring urban environmental pollution by bivariate control charts: New methodology and case study in Santiago, Chile," Environmetrics, John Wiley & Sons, Ltd., vol. 30(5), August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Marcelo Bourguignon & Diego I. Gallardo & Helton Saulo, 2024. "Parametric Quantile Beta Regression Model," International Statistical Review, International Statistical Institute, vol. 92(1), pages 106-129, April.
    5. Josmar Mazucheli & Bruna Alves & Mustafa Ç. Korkmaz & Víctor Leiva, 2022. "Vasicek Quantile and Mean Regression Models for Bounded Data: New Formulation, Mathematical Derivations, and Numerical Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    6. 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.
    7. 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.

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