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复合分位回归的贝叶斯经验似然推断

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  • 国家科技期刊平台
  • NETL
  • NSTL
  • 万方数据
本文将贝叶斯经验似然方法推广到复合分位数回归模型中。构造复合分位数回归模型的经验似然函数，在给定先验信息后，推导出未知参数的条件后验分布。考虑到未知参数后验分布形式较为复杂且有隐式方程约束，构造带约束条件的Metropolis-Hastings算法对模型参数进行点估计、置信区间估计及参数假设检验。计算机模拟仿真结果显示，当模型随机误差为厚尾分布时，贝叶斯经验似然复合分位回归法较复合分位回归法、分位回归法以及最小二乘法在估计偏差和方差上都有明显优势，尤其是数据含有较多异常点时，本文提出的方法最为稳健。利用新方法对一个医疗费用支出影响因素数据进行建模分析发现:较其他估计方法，无论是否删除数据中异常点，贝叶斯经验似然复合分位回归法得到的系数估计前后变化最小，这为实际建模过程时减少数据中未知异常点给模型带来的影响提供有益帮助。
Bayesian Empirical Likelihood Inference for Composite Quantile Regression
In this paper,the Bayesian empirical likelihood method is extended to the compound quantile regression model.Firstly,the empirical likelihood function of the compound quantile regression model is constructed,and the conditional posterior distribution of unknown parameters is derived after the prior information is given.Secondly,considering that the posterior distribution of unknown parameters is complex and has implicit equation constraints,a Metropolis-Hastings algorithm with constraints is constructed for point estimation,confidence interval estimation and parameter hypothesis testing of model parameters.The computer simulation results show that when the stochastic error of the model is a thick tail distribution,the Bayesian empirical likelihood compound quantile regression method proposed in this paper has more obvious advantages than the compound quantile regression method,the quantile regression method and the least square method in estimating deviation and variance.Especially when the data contains more anomalies,the proposed method is the most robust.Finally,the paper uses the new method to model and analyze the data of a medical expenditure influencing factor,and finds that compared with other estimation methods,the coefficient obtained by Bayes empirical likelihood compound quantile regression method changes the least before and after estimation,regardless of whether the abnormal points in the data are deleted or not.This provides useful assistance in reducing the impact of unknown outtiers in the date on the model during a real modeling process.

compound quantile regressionBayesian empirical likelihoodMetropolis-Hastings algorithmBayes factor

王景炜、胡超竹、李翰芳、罗幼喜

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湖北工业大学理学院,湖北武汉 430068

复合分位数回归 贝叶斯经验似然 Metropolis-Hastings算法 贝叶斯因子

国家自然科学基金青年基金湖北省教育厅人文社科重点项目湖北工业大学博士启动基金湖北省教育厅哲学社会科学基金

1170116120D043BSQD202010322Y059

2024

10.16088/j.issn.1001-6600.2023110304

广西师范大学学报(自然科学版)
广西师范大学

广西师范大学学报(自然科学版)

CSTPCD北大核心
影响因子：0.448
ISSN：1001-6600
年,卷(期)：2024.42(5)