ON THE ADAPTIVE ELASTIC-NET WITH A DIVERGING NUMBER OF PARAMETERS.

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property (Fan and Li, 2001; Fan and Peng, 2004) which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive Elastic-Net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive Elastic-Net. We show by simulations that the adaptive Elastic-Net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.

• Publication year

  2009

• Venue

  Annals of Statistics

• Publication date

  2009-08-13

• Fields of study

  Mathematics, Computer Science, Medicine

• Identifiers
  DOI 10.1214/08-AOS625arXiv 0908.1836PMID 20445770PMCID PMC2864037
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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