部分线性模型下Adaptive Dantzig Selector方法的渐近正态性
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摘要
变量选择是处理超高维数据过程中重要的部分.本文提出部分线性模型下ADS(Adaptive Dantzig Selector)方法,并证明其渐近正态性.通过数值模拟以及大众点评网数据,验证此方法的可行性以及高精准性.
Variable selection is an important part in the process of dealing with ultra high dimensional data.ADS(Adaptive Dantzig Selector) method under partial linear model is proposed and its asymptotic normality is proved. Numerical simulation and the data from dianping.com are verified the feasibility and high accuracy of the method.
Variable selection is an important part in the process of dealing with ultra high dimensional data.ADS(Adaptive Dantzig Selector) method under partial linear model is proposed and its asymptotic normality is proved. Numerical simulation and the data from dianping.com are verified the feasibility and high accuracy of the method.
引文
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[7]Li F.Variable selection and parameter estimation for partially linear models via Dantzig selector[J].Metrika,2013,76(2):225-238.
[8]Huang J,Ma S.Adaptive lasso for sparse high-dimensional regression models[J].Statistica Sinica,2006,18(4):1603-1618.
[9]Dicker L H.Regularized Regression Methods for Variable Selection and Estimation[D].Boston:Harvard University,2010.
[2]Zhao P,Yu B.Stagewise Lasso[J].Journal of Machine Learning Research,2014,8(12):2701-2726.
[3]Candes E,Tao T.The Dantzig Selector:statistical estimation when p is much larger than n[J].The Annals of Statistics,2007,35(6):2392-2404.
[4]Dicker L,Lin X.Parallelism,uniqueness,and large-sample asymptotics for the Dantzig selector[J].Canadian Journal of Statistics,2013,41(1):23-35.
[5]James G M,Radchenko P.A generalized Dantzig selector with shrinkage tuning[J].Biometrika,2009,96(2):323-337.
[6]董凯.高维数据部分线性模型的变量选择[D].北京:北京工业大学图书馆,2012.
[7]Li F.Variable selection and parameter estimation for partially linear models via Dantzig selector[J].Metrika,2013,76(2):225-238.
[8]Huang J,Ma S.Adaptive lasso for sparse high-dimensional regression models[J].Statistica Sinica,2006,18(4):1603-1618.
[9]Dicker L H.Regularized Regression Methods for Variable Selection and Estimation[D].Boston:Harvard University,2010.