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Quantile Estimation Based on the Log-Skew- t Linear Regression Model: Statistical Aspects, Simulations, and Applications

Author

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  • Raúl Alejandro Morán-Vásquez

    (Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia
    These authors contributed equally to this work.)

  • Anlly Daniela Giraldo-Melo

    (Instituto de Matemáticas, Universidad de Antioquia, Calle 67 No. 53-108, Medellín 050010, Colombia
    These authors contributed equally to this work.)

  • Mauricio A. Mazo-Lopera

    (Departamento de Estadística, Universidad Nacional de Colombia, Carrera 65 No. 59A-110, Medellín 050034, Colombia
    These authors contributed equally to this work.)

Abstract

We propose a robust linear regression model assuming a log-skew- t distribution for the response variable, with the aim of exploring the association between the covariates and the quantiles of a continuous and positive response variable under skewness and heavy tails. This model includes the log-skew-normal and log- t linear regression models as special cases. Our simulation studies indicate good performance of the quantile estimation approach and its outperformance relative to the classical quantile regression model. The practical applicability of our methodology is demonstrated through an analysis of two real datasets.

Suggested Citation

  • Raúl Alejandro Morán-Vásquez & Anlly Daniela Giraldo-Melo & Mauricio A. Mazo-Lopera, 2025. "Quantile Estimation Based on the Log-Skew- t Linear Regression Model: Statistical Aspects, Simulations, and Applications," Stats, MDPI, vol. 8(3), pages 1-16, July.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:58-:d:1700120
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    References listed on IDEAS

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    1. Adelchi Azzalini & Thomas Del Cappello & Samuel Kotz, 2002. "Log-Skew-Normal and Log-Skew-t Distributions as Models for Family Income Data," Journal of Income Distribution, Ad libros publications inc., vol. 11(3-4), pages 2-2, September.
    2. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
    3. Raúl Alejandro Morán-Vásquez & Anlly Daniela Giraldo-Melo & Mauricio A. Mazo-Lopera, 2023. "Quantile Estimation Using the Log-Skew-Normal Linear Regression Model with Application to Children’s Weight Data," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    4. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Riani, Marco & Atkinson, Anthony C. & Morelli, Gianluca & Corbellini, Aldo, 2025. "The use of modern robust regression analysis with graphics: an example from marketing," LSE Research Online Documents on Economics 126922, London School of Economics and Political Science, LSE Library.
    8. Card, David & Lemieux, Thomas, 1996. "Wage dispersion, returns to skill, and black-white wage differentials," Journal of Econometrics, Elsevier, vol. 74(2), pages 319-361, October.
    9. Marco Riani & Anthony C. Atkinson & Gianluca Morelli & Aldo Corbellini, 2025. "The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing," Stats, MDPI, vol. 8(1), pages 1-30, January.
    10. 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.
    11. Lidia de Castro Romero & Víctor Martín Barroso & Rosa Santero-Sánchez, 2023. "Does Gender Equality in Managerial Positions Improve the Gender Wage Gap? Comparative Evidence from Europe," Economies, MDPI, vol. 11(12), pages 1-23, December.
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