Prediction error property of the Lasso Estimator and its generalization

Huang, Fuchun 2003, Prediction error property of the Lasso Estimator and its generalization, Australian & New Zealand journal of statistics, vol. 45, no. 2, pp. 217-228, doi: 10.1111/1467-842X.00277.

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Title Prediction error property of the Lasso Estimator and its generalization
Author(s) Huang, Fuchun
Journal name Australian & New Zealand journal of statistics
Volume number 45
Issue number 2
Start page 217
End page 228
Publisher Wiley-Blackwell Publishing Asia
Place of publication Richmond, Vic.
Publication date 2003
ISSN 1369-1473
Summary 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.
Language eng
DOI 10.1111/1467-842X.00277
Field of Research 010405 Statistical Theory
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2003, Australian Statistical Publishing Association Inc.
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