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Prediction Error Property of the Lasso Estimator and its Generalization

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  • Fuchun Huang

Abstract

The lasso procedure is an estimator‐shrinkage and variable selection method. This paper shows that there always exists an interval of tuning parameter values such that the corresponding mean squared prediction error for the lasso estimator is smaller than for the ordinary least squares estimator. For an estimator satisfying some condition such as unbiasedness, the paper defines the corresponding generalized lasso estimator. Its mean squared prediction error is shown to be smaller than that of the estimator for values of the tuning parameter in some interval. This implies that all unbiased estimators are not admissible. Simulation results for five models support the theoretical results.

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  • Fuchun Huang, 2003. "Prediction Error Property of the Lasso Estimator and its Generalization," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 217-228, June.
    • Handle: RePEc:bla:anzsta:v:45:y:2003:i:2:p:217-228
    DOI: 10.1111/1467-842X.00277
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    Cited by:

    1. Yoonsuh Jung, 2018. "Multiple predicting K-fold cross-validation for model selection," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 197-215, January.
    2. Ismail Shah & Hina Naz & Sajid Ali & Amani Almohaimeed & Showkat Ahmad Lone, 2023. "A New Quantile-Based Approach for LASSO Estimation," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    3. Kei Hirose & Miyuki Imada, 2018. "Sparse factor regression via penalized maximum likelihood estimation," Statistical Papers, Springer, vol. 59(2), pages 633-662, June.

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