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On grouping effect of elastic net

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  • Zhou, Ding-Xuan

Abstract

Grouping effect of the elastic net asserts that coefficients corresponding to highly correlated predictors in a linear regression setting have small differences. A quantitative estimate for such small differences was given in Zou and Hastie (2005) when the coefficients have the same sign. We show that the same estimate holds true even when the coefficients have different signs. The estimate is also improved by means of an empirical approximation error when the model fits the data well.

Suggested Citation

  • Zhou, Ding-Xuan, 2013. "On grouping effect of elastic net," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2108-2112.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2108-2112
    DOI: 10.1016/j.spl.2013.05.014
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    References listed on IDEAS

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    1. Ming Yuan & Yi Lin, 2007. "On the non‐negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161, April.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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