<p>In this paper, we propose a nonparametric Bayesian estimation and model selection method for additive models based on weighted composite quantile regression. This method identifies the unknown smooth functions of the additive model as linear, nonlinear, or zero components by setting a multiplicative parameterized spike-slab prior distribution, which solves the problem of selecting predictive variable components in partially linear additive models when prior information is insufficient. In addition, it further generalizes the composite quantile regression to additive models by combining information from multiple quantiles. A Bayesian hierarchical model is established based on the mixed representation of the asymmetric Laplace distribution, and the posterior distributions of all unknown parameters are sampled by Markov chain Monte Carlo (MCMC). Finally, in the simulation and real data analysis, the variable selection results, root mean square error and other indicators are used to further prove that the method is more competitive than the existing methods.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Bayesian additive weighted composite quantile regression

  • Yonggang Ji,
  • Mian Wang,
  • Maoyuan Zhou

摘要

In this paper, we propose a nonparametric Bayesian estimation and model selection method for additive models based on weighted composite quantile regression. This method identifies the unknown smooth functions of the additive model as linear, nonlinear, or zero components by setting a multiplicative parameterized spike-slab prior distribution, which solves the problem of selecting predictive variable components in partially linear additive models when prior information is insufficient. In addition, it further generalizes the composite quantile regression to additive models by combining information from multiple quantiles. A Bayesian hierarchical model is established based on the mixed representation of the asymmetric Laplace distribution, and the posterior distributions of all unknown parameters are sampled by Markov chain Monte Carlo (MCMC). Finally, in the simulation and real data analysis, the variable selection results, root mean square error and other indicators are used to further prove that the method is more competitive than the existing methods.