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

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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. 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.
    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.
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    7. 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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