二元选择分位回归的自适应LASSO改进
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摘要
为避免模型出现过拟合,将自适应LASSO变量选择方法引入二元选择分位回归模型,利用贝叶斯方法构建Gibbs抽样算法并在抽样中设置不影响预测结果的约束条件‖β‖=1以提高抽样值的稳定性.通过数值模拟,表明改进的模型有更为良好的参数估计效率、变量选择功能和分类能力.
Binary quantile regression model with the adaptive LASSO penalty is proposed for overfitting problems by presenting a Bayesian Gibbs sampling algorithm to estimate parameters.In the process of sampling,the restriction on‖β‖ =1 is motivated to improve the stability of the sampling values.Numerical analysis show there are better improvements of the proposed method in parameter estimation,variable selection and classification.
Binary quantile regression model with the adaptive LASSO penalty is proposed for overfitting problems by presenting a Bayesian Gibbs sampling algorithm to estimate parameters.In the process of sampling,the restriction on‖β‖ =1 is motivated to improve the stability of the sampling values.Numerical analysis show there are better improvements of the proposed method in parameter estimation,variable selection and classification.
引文
[1]Roger Koenker,Gilbert Bassett,Regression Quantiles[J].Econometrica,1978,46(1):33-50.
[2]Charles F.Manski,Maximum score estimation of the stochastic utility model of choice[J].Journal of Econometrics,1975,3(3):205-228.
[3]Keming Yu,Rana A.Moyeed,Bayesian quantile regression[J].Statistics&probability Letters,2001,54(4):437-447.
[4]Dries F.Benoit,Dirk Van den Poel,Binary quantile regression:a Bayesian approach based on the asymmetric Laplace distribution[J].Journal of Applied Econometrics,2012,27(7):1174-1188.
[5]Robert Tibshirani,Regression shrinkage and selection via the LASSO[J].Journal of the Royal Statistical Society,Series B,1996,58(1):267-288.
[6]Hui Zou,The adaptive LASSO and its oracle properties[J].Journal of the American Statistical Association,2006,101(476):1418-1429.
[7]Dries F.Benoit,Rahim Alhamzawi,Keming Yu,Bayesian lasso binary quantile regression[J].Computational Statistics,2013,28(6):2861-2873.
[8]Hussein Hashem,Veronica Vinciontti,Rahim Alhamzawi,Keming Yu.,Quantile regression with group lasso for classification[J].Advances in Data Analysis and Classification,2016,10(3):375-390.
[9]Yonggang Ji,Nan Lin,Baoxue Zhang,Model selection in binary and tobit quantile regression using the Gibbs sampler[J].Computational Statistics&Data Analysis,2012,56(4):827-839.
[10]Beong In Yun,Transformation methods for finding multiple roots of nonlinear equations[J].Applied Mathematics and Computation,2010,217(2):599-606.
[2]Charles F.Manski,Maximum score estimation of the stochastic utility model of choice[J].Journal of Econometrics,1975,3(3):205-228.
[3]Keming Yu,Rana A.Moyeed,Bayesian quantile regression[J].Statistics&probability Letters,2001,54(4):437-447.
[4]Dries F.Benoit,Dirk Van den Poel,Binary quantile regression:a Bayesian approach based on the asymmetric Laplace distribution[J].Journal of Applied Econometrics,2012,27(7):1174-1188.
[5]Robert Tibshirani,Regression shrinkage and selection via the LASSO[J].Journal of the Royal Statistical Society,Series B,1996,58(1):267-288.
[6]Hui Zou,The adaptive LASSO and its oracle properties[J].Journal of the American Statistical Association,2006,101(476):1418-1429.
[7]Dries F.Benoit,Rahim Alhamzawi,Keming Yu,Bayesian lasso binary quantile regression[J].Computational Statistics,2013,28(6):2861-2873.
[8]Hussein Hashem,Veronica Vinciontti,Rahim Alhamzawi,Keming Yu.,Quantile regression with group lasso for classification[J].Advances in Data Analysis and Classification,2016,10(3):375-390.
[9]Yonggang Ji,Nan Lin,Baoxue Zhang,Model selection in binary and tobit quantile regression using the Gibbs sampler[J].Computational Statistics&Data Analysis,2012,56(4):827-839.
[10]Beong In Yun,Transformation methods for finding multiple roots of nonlinear equations[J].Applied Mathematics and Computation,2010,217(2):599-606.