Post[script l]1penalized estimators in highdimensional linear regression models
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The work Post[script l]1penalized estimators in highdimensional linear regression models represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Post[script l]1penalized estimators in highdimensional linear regression models
Resource Information
The work Post[script l]1penalized estimators in highdimensional linear regression models represents a distinct intellectual or artistic creation found in Boston University Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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 Post[script l]1penalized estimators in highdimensional linear regression models
 Statement of responsibility
 Alexandre Belloni [and] Victor Chernozhukov
 Title variation
 PostLASSOpenalized estimators in highdimensional linear regression models
 Language
 eng
 Summary
 In this paper we study postpenalized estimators which apply ordinary, unpenalized linear regression to the model selected by firststep penalized estimators, typically LASSO. It is well known that LASSO can estimate the regression function at nearly the oracle rate, and is thus hard to improve upon. We show that postLASSO performs at least as well as LASSO in terms of the rate of convergence, and has the advantage of a smaller bias. Remarkably, this performance occurs even if the LASSObased model selection fails in the sense of missing some components of the true regression model. By the true model we mean here the best sdimensional approximation to the regression function chosen by the oracle. Furthermore, postLASSO can perform strictly better than LASSO, in the sense of a strictly faster rate of convergence, if the LASSObased model selection correctly includes all components of the true model as a subset and also achieves a sufficient sparsity. In the extreme case, when LASSO perfectly selects the true model, the postLASSO estimator becomes the oracle estimator. An important ingredient in our analysis is a new sparsity bound on the dimension of the model selected by LASSO which guarantees that this dimension is at most of the same order as the dimension of the true model. Our rate results are nonasymptotic and hold in both parametric and nonparametric models. Moreover, our analysis is not limited to the LASSO estimator in the first step, but also applies to other estimators, for example, the trimmed LASSO, Dantzig selector, or any other estimator with good rates and good sparsity. Our analysis covers both traditional trimming and a new practical, completely datadriven trimming scheme that induces maximal sparsity subject to maintaining a certain goodnessoffit. The latter scheme has theoretical guarantees similar to those of LASSO or postLASSO, but it dominates these procedures as well as traditional trimming in a wide variety of experiments. Keywords: LASSO, postLASSO, postmodelselection estimators. JEL Classifications: 62H12, 62J99, 62J07
 Cataloging source
 MYG
 Illustrations
 illustrations
 Index
 no index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 technical reports
 Series statement
 Working paper series / Massachusetts Institute of Technology, Dept. of Economics
 Series volume
 working paper 105 [2010 revision]
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