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The adaptive LASSO and its oracle properties
| Venue: | Journal of the American Statistical Association |
| Citations: | 681 - 11 self |
BibTeX
@ARTICLE{Zou_theadaptive,
author = {Hui Zou},
title = {The adaptive LASSO and its oracle properties},
journal = {Journal of the American Statistical Association},
year = {},
pages = {2006}
}
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Abstract
The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the!1 penalty. We show that the adaptive lasso enjoys the oracle properties; namely, it performs as well as if the true underlying model were given in advance. Similar to the lasso, the adaptive lasso is shown to be near-minimax optimal. Furthermore, the adaptive lasso can be solved by the same efficient algorithm for solving the lasso. We also discuss the extension of the adaptive lasso in generalized linear models and show that the oracle properties still hold under mild regularity conditions. As a byproduct of our theory, the nonnegative garotte is shown to be consistent for variable selection.
Keyphrases
adaptive lasso oracle property variable selection lasso variable selection different coefficient popular technique generalized linear model adaptive weight new version certain scenario true underlying model mild regularity condition nonnegative garotte necessary condition certain condition simultaneous estimation efficient algorithm
