CiteWeb id: 20120000091

CiteWeb score: 2743

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 l1 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 bypro...

The publication "The adaptive lasso and its oracle properties" is placed in the Top 10000 of the best publications in CiteWeb. Also in the category Mathematics it is included to the Top 1000. Additionally, the publicaiton "The adaptive lasso and its oracle properties" is placed in the Top 100 among other scientific works published in 2012.
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