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On the non-negative garrotte estimator

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  • Ming Yuan
  • Yi Lin
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    Abstract

    We study the non-negative garrotte estimator from three different aspects: consistency, computation and flexibility. We argue that the non-negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form. In particular, we consider using the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non-negative garrotte. We prove that the non-negative garrotte has the nice property that, with probability tending to 1, the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables, whereas such a property may not be valid for the initial estimators. In general, we show that the non-negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection. We also show that the non-negative garrotte has a piecewise linear solution path. Using this fact, we propose an efficient algorithm for computing the whole solution path for the non-negative garrotte. Simulations and a real example demonstrate that the non-negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy. Copyright 2007 Royal Statistical Society.

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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2007.00581.x
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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 69 (2007)
    Issue (Month): 2 ()
    Pages: 143-161

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    Handle: RePEc:bla:jorssb:v:69:y:2007:i:2:p:143-161

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    Cited by:
    1. Anestis Antoniadis & Irène Gijbels & Mila Nikolova, 2011. "Penalized likelihood regression for generalized linear models with non-quadratic penalties," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 585-615, June.
    2. Daye, Z. John & Jeng, X. Jessie, 2009. "Shrinkage and model selection with correlated variables via weighted fusion," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1284-1298, February.
    3. Huyn Hak Kim & Norman R. Swanson, 2011. "Forecasting Financial and Macroeconomic Variables Using Data Reduction Methods: New Empirical Evidence," Departmental Working Papers 201119, Rutgers University, Department of Economics.

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