QQ客服 官方微博 反馈留言

	Asymptotic properties of Lasso plus mLS and Lasso plus Ridge in sparse high-dimensional linear regression
	Liu, Hanzhong
	2013
关键词	Lasso irrepresentable condition Lasso-fmLS and Lasso plus Ridge sparsity asymptotic unbiasedness asymptotic normality residual bootstrap VARIABLE SELECTION MODEL SELECTION ADAPTIVE LASSO ORACLE PROPERTIES RECOVERY ESTIMATORS REPRESENTATIONS BOOTSTRAP TESTS
英文摘要	We study the asymptotic properties of Lasso+mLS and Lasso+ Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+ rriLS and Lasso+Ridge. Second, we derive the asymptotic unbiasedness of Lasso rilLS and Lasso Ridge. More specifically, we show that their biases decay at an exponential rate and they can achieve the oracle convergence rate of sln. (where s is the number of nonzero regression coefficients and 12 is the sample size) for mean squared error (MSE). Third, we show that Lasso mLS and Lasso Ridge are asymptotically normal. They have an oracle property in the sense that they can select the true predictors with probability converging to 1 and the estimates of nonzero parameters have the same asymptotic normal distribution that they would have if the zero parameters were known in advance. In fact, our analysis is not limited to adopting Lasso in the selection stage, but is applicable to any other model selection criteria with exponentially decay rates of the probability of selecting wrong models.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000329800200001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Statistics & Probability; SCI(E); 7; ARTICLE; 3124-3169; 7
语种	英语
出处	SCI
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314357]
专题	数学科学学院
推荐引用方式 GB/T 7714	Liu, Hanzhong. Asymptotic properties of Lasso plus mLS and Lasso plus Ridge in sparse high-dimensional linear regression. 2013-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。