基于Bayesian Bootstrap抽样的高维线性回归模型  

High Dimensional Linear Regression Model Based on Bayesian Bootstrap Sampling

作　　者：周超 吴娟[1] ZHOU Chao;WU Juan(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,Hubei,China)

机构地区：[1]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《武汉大学学报（理学版）》2021年第5期461-466,共6页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(41972319);中国高等教育学会理科教育专业委员会高等理科教育研究课题(20ZSLKJYYB32);华中科技大学教学研究项目(2020100)。

摘　　要：研究小样本下高维线性回归模型中的变量选择问题和模型预测能力。当自变量维数p远大于样本量n时,提出基于Bayesian bootstrap抽样的SCAD(smoothly clipped absolute deviation)压缩方法。仿真和实证分析表明,与SCAD和LASSO(least absolute shrinkage and selection operator)两种传统回归压缩方法相比,本算法受随机干扰影响较小。当样本量较小时,本算法的变量压缩结果更好,变量选择能力更强,模型的标准均方误差值也最小,且模型预测能力提升明显。The variable selection is proposed and the prediction ability of high dimensional linear regression model under small sample size is studied.When the dimension of independent variable p is much larger than the sample size n,the SCAD(smoothly clipped absolute deviation)compression method based on Bayesian bootstrap sampling is proposed.Simulation and empirical analysis show that the algorithm is less affected by random interference than SCAD and LASSO(least absolute shrink and selection operator),two traditional regression compression methods.It shows that the smaller the sample size,the better the result of compression of variables,the stronger the ability of variable selection,and the smaller the normalized mean square error of the model,and the prediction ability of the model is improved significantly.

关 键 词：高维线性回归 变量选择 小样本 Bayesian bootstrap LASSO(least absolute shrinkage and selection operator) SCAD(smoothly clipped absolute deviation) 

分 类 号：O213.9[理学—概率论与数理统计]