A semiparametric approach for joint modeling of median and skewness

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• 作者：Luis Hernando Vanegas (1) (2)
  Gilberto A. Paula (1)
  
  1. Instituto de Matem谩tica e Estat铆stica ; Universidade de S茫o Paulo ; S茫o Paulo ; Brazil
  2. Departamento de Estad铆stica ; Universidad Nacional de Colombia ; Bogot谩 ; Colombia
  
• 关键词：Skewness ; Asymmetric responses ; Maximum penalized likelihood estimates ; Semiparametric models ; Robust estimates ; Natural cubic spline ; 62J02 ; 62G08 ; 62J20
• 刊名：TEST
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：24
• 期：1
• 页码：110-135
• 全文大小：679 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistical Theory and Methods
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1863-8260

文摘

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.