摘要
回归模型一般采取传统的最小二乘估计(LSE)方法,然而当数据包含非正态特征或异常值时该估计方法会导致不稳健的参数估计.与LSE方法相比,即使出现非正态误差或异常数据,复合分位回归(CQR)方法也能提供更稳健的估计结果.基于复合反对称拉普拉斯分布(CALD),本文提出了贝叶斯框架下的加权复合分量回归(WCQR)方法.正则化方法已经被验证可以有效处理高维稀疏回归模型,它可以同时进行变量选择和参数估计.本文结合贝叶斯LASSO正则化方法和WCQR方法来拟合线性回归模型,建立了WCQR的贝叶斯LASSO正则化分层模型,并导出了所有参数的条件后验分布以进行统计推断.最后,通过蒙特卡罗模拟和实际数据分析演示了所提出方法.
Regression models are traditionally estimated using the least square estimation(LSE)method which may result in non-robust parameter estimates when data includes non-normal feature or outliers.Compared to LSE approach,composite quantile regression(CQR)can provide more robust estimation results even suffering non-normal errors or outliers.Based on a composite asymmetric Laplace distribution(CALD),the weighted composite quantile regression(WCQR)can be treated in the Bayesian framework.Regularization methods have been verified to be very effective for high-dimensional sparse regression models in that it can simultaneously conduct variable selection and parameters estimation.In this paper,we combine Bayesian LASSO regularization methods with WCQR to fit linear regression models.Bayesian LASSO-regularized hierarchical models of WCQR are constructed and the conditional posterior distributions of all unknown parameters are derived to conduct statistical inference.Finally,the developed methods are illustrated by Monte Carlo simulations and a real data analysis.
作者
田玉柱
田茂再
TIAN Yuzhu;TIAN Maozai(School of Mathematics and Statistics,Northwest Normal University,Lanzhou,730070,China;School of Statistics,Renmin University of China,BeiJing,100872,China)
出处
《应用概率统计》
CSCD
北大核心
2021年第4期390-404,共15页
Chinese Journal of Applied Probability and Statistics
基金
supported by the National Natural Science Foundation of China(Grant Nos.11501167,11861042).
