Bayesian quantile regression for partially linear additive models

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• 作者：Yuao Hu (1)
  Kaifeng Zhao (1)
  Heng Lian (1)
  
  1. Division of Mathematical Sciences ; School of Physical and Mathematical Sciences ; Nanyang Technological University ; Singapore ; 637371 ; Singapore
  
• 关键词：Additive models ; Markov chain Monte Carlo ; Quantile regression ; Variable selection
• 刊名：Statistics and Computing
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：25
• 期：3
• 页码：651-668
• 全文大小：1,179 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics Computing and Software
  Statistics
  Numeric Computing
  Mathematics
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-1375

文摘

In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian inferences of quantile regression models based on the check loss. The advantage of this new method is that nonlinear, linear and zero function components can be separated automatically and simultaneously during model fitting without the need of pre-specification or parameter tuning. This is achieved by spike-and-slab priors using two sets of indicator variables. For posterior inferences, we design an effective partially collapsed Gibbs sampler. Simulation studies are used to illustrate our algorithm. The proposed approach is further illustrated by applications to two real data sets.