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Asymptotic properties of the residual bootstrap for Lasso estimators
Author(s):
A.
Chatterjee;
S.
N.
Lahiri
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4497-4509.
MSC (2010):
Primary 62J07;
Secondary 62G09, 62E20
Posted:
July 9, 2010
MathSciNet review:
2680074
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Abstract:
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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Additional Information:
A.
Chatterjee
Affiliation:
Department of Statistics, Texas A&M University, College Station, Texas 77843-3143
Email:
cha@stat.tamu.edu
S.
N.
Lahiri
Affiliation:
Department of Statistics, Texas A&M University, College Station, Texas 77843-3143
Email:
snlahiri@stat.tamu.edu
DOI:
10.1090/S0002-9939-2010-10474-4
PII:
S 0002-9939(2010)10474-4
Keywords:
Consistency,
bootstrap,
penalized regression,
random measure
Received by editor(s):
January 22, 2009
Received by editor(s) in revised form:
December 23, 2009 and March 2, 2010
Posted:
July 9, 2010
Additional Notes:
This research was partially supported by NSF grant DMS-0707139.
Communicated by:
Edward C. Waymire
Copyright of article:
Copyright
2010,
American Mathematical Society
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