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Title:Penalized estimation of high-dimensional models under a generalized sparsity condition PDF Logo
Authors:Horowitz, Joel
Huang, Jian
Issue Date:2012
Series/Report no.:cemmap working paper CWP17/12
Abstract:We consider estimation of a linear or nonparametric additive model in which a few coefficients or additive components are large and may be objects of substantive interest, whereas others are small but not necessarily zero. The number of small coefficients or additive components may exceed the sample size. It is not known which coefficients or components are large and which are small. The large coefficients or additive components can be estimated with a smaller mean-square error or integrated mean-square error if the small ones can be identified and the covariates associated with them dropped from the model. We give conditions under which several penalized least squares procedures distinguish correctly between large and small coefficients or additive components with probability approaching 1 as the sample size increases. The results of Monte Carlo experiments and an empirical example illustrate the benefits of our methods.
Subjects:penalized regression
high-dimensional data
variable selection
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2012.1712
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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