Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 138, Issue 12, Pages 4497-4509Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9939-2010-10474-4
Keywords
Consistency; bootstrap; penalized regression; random measure
Categories
Funding
- NSF [DMS-0707139]
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In this article, we derive the asymptotic distribution of the bootstrapped Lasso estimator of the regression parameter in a multiple linear regression model. It is shown that under some mild regularity conditions on the design vectors and the regularization parameter, the bootstrap approximation converges weakly to a random measure. The convergence result rigorously establishes a previously known heuristic formula for the limit distribution of the bootstrapped Lasso estimator. It is also shown that when one or more components of the regression parameter vector are zero, the bootstrap may fail to be consistent.
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