On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding

Benedikt Pötscher and Hannes Leeb ()

MPRA Paper from University Library of Munich, Germany

Abstract: We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent model selection and for the case where the estimators are tuned to perform conservative model selection. Our findings complement those of Knight and Fu (2000) and Fan and Li (2001). We show that the distributions are typically highly nonnormal regardless of how the estimator is tuned, and that this property persists in large samples. An impossibility result regarding estimation of the estimators' distribution function is also provided.

Keywords: Penalized maximum likelihood; LASSO; SCAD; thresholding; post-model-selection estimator; finite-sample distribution; asymptotic distribution; estimation of distribution; uniform consistency (search for similar items in EconPapers)
JEL-codes: C13 C2 (search for similar items in EconPapers)
Date: 2007-10
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (7)

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https://mpra.ub.uni-muenchen.de/14708/2/MPRA_paper_14708.pdf revised version (application/pdf)

Related works:
Journal Article: On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:5615

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