A semiparametric approach for joint modeling of median and skewness

Luis Vanegas () and Gilberto Paula ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 24, issue 1, 110-135

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

Keywords: Skewness; Asymmetric responses; Maximum penalized likelihood estimates; Semiparametric models; Robust estimates; Natural cubic spline; 62J02; 62G08; 62J20 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:24:y:2015:i:1:p:110-135

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DOI: 10.1007/s11749-014-0401-7

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