On the distribution of the adaptive LASSO estimator

Benedikt Pötscher and Ulrike Schneider

MPRA Paper from University Library of Munich, Germany

Abstract: We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than n^{-1/2} in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the `oracle' property of the adaptive LASSO estimator established in Zou 2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator.

Keywords: Penalized maximum likelihood; LASSO; adaptive LASSO; nonnegative garotte; finite-sample distribution; asymptotic distribution; oracle property; estimation of distribution; uniform consistency (search for similar items in EconPapers)
JEL-codes: C13 C20 C51 C52 (search for similar items in EconPapers)
Date: 2007-12
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:6913

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