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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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\begin{center}
  4:15 p.m., Tuesday, January 16, 2007\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Nicolai Meinshausen} \\
Department of Statistics\\
University of California, Berkeley
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  \textbf{Some Consistency Results for Lasso Variable Selection}
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\noindent
It has been shown recently that the Lasso can be sign consistent
for linear regression --picking exactly the right variables-- only
under a restrictive condition on the design matrix. I will give some
geometric illustration of these results. Even if the condition is not
fulfilled, it can be shown that the Lasso estimator chooses
the important variables with high probability. The estimate is moreover close
to the true vector in an l2-norm sense.
Two-stage procedures can achieve consistent model selection,
taking the Lasso as a first initial estimator which is refined
and improved upon in a second stage.

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