We consider the asymptotic behavior ofregression estimators that
minimize the residual sum of squares plus a penalty proportional to
$\sum|\beta_j|^{\gamma}$. for some $\gamma > 0$. These estimators include
the Lasso as a special case when $\gamma = 1$. Under appropriate conditions, we
show that the limiting distributions can have positive probability mass at 0
when the true value of the parameter is 0.We also consider asymptotics for
“nearly singular” designs.
Publié le : 2000-10-14
Classification:
Penalized regression,
Lasso,
shrinkage estimation,
epi-convergence in distribution,
62J05,
62J07,
62E20,
60F05
@article{1015957397,
author = {Knight, Keith and Fu, Wenjiang},
title = {Asymptotics for lasso-type estimators},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 1356-1378},
language = {en},
url = {http://dml.mathdoc.fr/item/1015957397}
}
Knight, Keith; Fu, Wenjiang. Asymptotics for lasso-type estimators. Ann. Statist., Tome 28 (2000) no. 3, pp. 1356-1378. http://gdmltest.u-ga.fr/item/1015957397/