Expectile回归模型的贝叶斯统计推断研究  

Bayesian Statistical Inference of Expectile Regression Model

作　　者：金娇 管思晴 扈灵嫣 张凯琦 吕洋 

机构地区：[1]北京工业大学,北京

出　　处：《统计学与应用》2021年第5期929-939,共11页Statistical and Application

摘　　要：目前,对于回归模型的主要关注点在于,通过描述响应变量分布更一般的特性,扩展具有可行性的(均值)回归模型。本文将利用expectile函数为基础,在贝叶斯的框架下,假设先验函数为正态分布,非对称广义高斯分布为似然分布,建立贝叶斯expectile回归模型,推导了贝叶斯expectile回归的估计方法。本文利用R语言对模型进行了数据模拟和实证分析,利用Metropolis-Hastings算法对目标后验函数进行抽样,从而得出参数的估计,结果表示贝叶斯expectile回归模型具有一定的可行性和准确性。本文还将贝叶斯expectile回归模型应用于美国人口调查工资数据(Berndt, 1991),对数据进行了回归拟合并计算出置信区间,结果表明,职业、受教育年限等因素对工资存在显著的影响。Currently, the main focus for regression models is to extend available (mean) regression models by describing more general properties of the distribution of the response variables. Under the framework of Bayes, based on the expectil, this paper builds the Bayesian expectile regression model which assumes that the prior function is normal distribution and the asymmetric generalized Gaussian distribution is likelihood distribution. Also, this paper deduces the estimation method of Bayesian expectile regression. This paper uses R language for data simulation and empirical analysis of the model where the Metropolis-Hastings algorithm is used to sample the target posterior function, so as to obtain the parameter estimation. The results show that the Bayesian expectile regression model has certain feasibility and accuracy. In this paper, the Bayesian expectile regression model is applied to the salary data of the United States Population Survey (Berndt, 1991), the confidence interval is calculated and the data is fitted by the regression. The results show that occupation, years of education and other factors have a significant impact on the salary.

关 键 词：贝叶斯 expectile 非对称广义高斯分布 Metropolis-Hastings算法 R语言 

分 类 号：G63[文化科学—教育学]