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A semiparametric approach for joint modeling of median and skewness

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  • Luis Vanegas
  • Gilberto Paula

Abstract

We motivate this paper by showing through Monte Carlo simulation that ignoring the skewness of the response variable distribution in non-linear regression models may introduce biases on the parameter estimates and/or on the estimation of the associated variability measures. Then, we propose a semiparametric regression model suitable for data set analysis in which the distribution of the response is strictly positive and asymmetric. In this setup, both median and skewness of the response variable distribution are explicitly modeled, the median using a parametric non-linear function and the skewness using a semiparametric function. The proposed model allows for the description of the response using the log-symmetric distribution, which is a generalization of the log-normal distribution and is flexible enough to consider bimodal distributions in special cases as well as distributions having heavier or lighter tails than those of the log-normal one. An iterative estimation process as well as some diagnostic methods are derived. Two data sets previously analyzed under parametric models are reanalyzed using the proposed methodology. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Luis Vanegas & Gilberto Paula, 2015. "A semiparametric approach for joint modeling of median and skewness," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 110-135, March.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:1:p:110-135
    DOI: 10.1007/s11749-014-0401-7
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    References listed on IDEAS

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    6. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
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    10. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
    11. Cysneiros, Francisco José A. & Vanegas, Luis Hernando, 2008. "Residuals and their statistical properties in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3269-3273, December.
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    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 & Jeremias Leão, 2017. "On log-symmetric duration models applied to high frequency financial data," Economics Bulletin, AccessEcon, vol. 37(2), pages 1089-1097.
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    5. 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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