Slides

12
Asymptotic Properties of the Dantzig Selector
• If C = lim n→∞ n −1 X T X is not parallel to the L 1 -ball.
• Asymptotic Limit: If λ/n → c 0 and c 0 ∈ [0, ∞], then ˆβ P → β ∗ ,
where β ∗ is the true value of β and β 0 solves
minimize ||β|| 1
subject to ||C(β ∗ − β)|| ∞ ≤ c 0 .
March, 2009
Xihong Lin