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CATEGORIES:Statistics
SUMMARY:On the Distribution of the Adaptive LASSO Estimato
r - Ulrike Schneider (University of Goettingen)
DTSTART;TZID=Europe/London:20100122T153000
DTEND;TZID=Europe/London:20100122T163000
UID:TALK22577AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/22577
DESCRIPTION:Penalized least squares (or maximum likelihood) es
timators\, such as\nthe famous LASSO\, have been s
tudied intensively in the last few years.\nWhile m
any properties of these estimators are now well un
derstood\, the\nunderstanding of their distributio
nal characteristics\, such as\nfinite-sample and l
arge-sample limit distributions\, is still\nincomp
lete.\n\nWe study the distribution of the adaptive
LASSO estimator (a variant\nof the LASSO introduc
ed by Zou\, 2006) for an orthogonal normal linear\
nregression model in finite samples as well as in
the large-sample\nlimit. We show that these distri
butions are typically highly\nnon-normal regardles
s of the choice of tuning of the estimator. The\nu
niform convergence rate is obtained and shown to b
e slower than\n$n^{-1/2}$ in case the estimator is
tuned to perform consistent model\nselection. Mor
eover\, we derive confidence intervals based on th
e\nadaptive LASSO\, compare their lenghts to the o
ne based on the\nunpenalized estimator and also di
scuss the questionable statistical\nrelevance of t
he 'oracle'-property of this estimator. Finally\,
we\nprovide an impossibility result regarding the
estimation of the\ndistribution function of the ad
aptive LASSO estimator.\n\njoint work with B.M. Po
tscher (University of Vienna)\n\nhttp://stochastik
.math.uni-goettingen.de/~schneider/\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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