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SUMMARY:On the Distribution of the Adaptive LASSO Estimator - Ulrike Schne
 ider (University of Goettingen)
DTSTART:20100122T153000Z
DTEND:20100122T163000Z
UID:TALK22577@talks.cam.ac.uk
CONTACT:8047
DESCRIPTION:Penalized least squares (or maximum likelihood) estimators\, s
 uch as\nthe famous LASSO\, have been studied intensively in the last few y
 ears.\nWhile many properties of these estimators are now well understood\,
  the\nunderstanding of their distributional characteristics\, such as\nfin
 ite-sample and large-sample limit distributions\, is still\nincomplete.\n\
 nWe study the distribution of the adaptive LASSO estimator (a variant\nof 
 the LASSO introduced by Zou\, 2006) for an orthogonal normal linear\nregre
 ssion model in finite samples as well as in the large-sample\nlimit. We sh
 ow that these distributions are typically highly\nnon-normal regardless of
  the choice of tuning of the estimator. The\nuniform convergence rate is o
 btained and shown to be slower than\n$n^{-1/2}$ in case the estimator is t
 uned to perform consistent model\nselection. Moreover\, we derive confiden
 ce intervals based on the\nadaptive LASSO\, compare their lenghts to the o
 ne based on the\nunpenalized estimator and also discuss the questionable s
 tatistical\nrelevance of the 'oracle'-property of this estimator. Finally\
 , we\nprovide an impossibility result regarding the estimation of the\ndis
 tribution function of the adaptive LASSO estimator.\n\njoint work with B.M
 . Potscher (University of Vienna)\n\nhttp://stochastik.math.uni-goettingen
 .de/~schneider/\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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