Cited by 7,470Statistical Methods and InferenceAdvanced Statistical Methods and ModelsSparse and Compressive Sensing Techniques

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The Adaptive Lasso and Its Oracle Properties

Zou, Hui·2006·Journal of the American Statistical Association

DOI 10.1198/016214506000000735

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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 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 byproduct of our theory, the nonnegative garotte is shown to be consistent for variable selection.

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Authors: Zou, H.
Affiliations: University of Minnesota (US)
Corresponding author: Zou, Hui
ORCID: Zou, Hui
Venue: Journal of the American Statistical Association
Publisher: Informa UK Limited
Published: 2006-12-01
Volume: 101
Issue: 476
Pages: 1418-1429
ISSN: 0162-1459 (ISSN-L)
1537-274X
DOI: 10.1198/016214506000000735
OpenAlex: W2020925091
Cited by: 7,470
References: 23
Citations by year: 2026: 324 · 2025: 476 · 2024: 474 · 2023: 454 · 2022: 567 · 2021: 639 · 2020: 528 · 2019: 548 · 2018: 473 · 2017: 443 · 2016: 416 · 2015: 388 · 2014: 385 · 2013: 361 · 2012: 304
FWCI: 76.03
Type: journal article
Language: en
Open access: closed
Locations: Journal of the American Statistical Association (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Physical Sciences › Computer Science › Signal Processing › Sparse and Compressive Sensing Techniques
Keywords: adaptive LASSO, LASSO, feature selection, oracle property, consistency, adaptive weighting, l1 penalty, generalized linear models

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The Adaptive Lasso and Its Oracle Properties

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