TY - JOUR
T1 - Optimal regression parameter-specific shrinkage by plug-in estimation
AU - Jung, Yoonsuh
PY - 2019/1/1
Y1 - 2019/1/1
N2 - One benefit of the bias-variance tradeoff is that regression estimators do not have to be strictly unbiased. However, to take full advantage of allowing bias, shrinkage regression estimators require that the appropriate level of bias is chosen carefully. Because the conventional grid search for the shrinkage parameters requires heavy computation, it is practically difficult to incorporate more than two shrinkage parameters. In this paper, we propose a class of shrinkage regression estimators which differently shrink each regression parameter. For this purpose, we set the number of shrinkage parameters to be the same as the number of regression coefficients. The ideal shrinkage for each parameter is suggested, meaning that a burdensome tuning process is not required for each parameter. The (Formula presented.) -consistency and oracle property of the suggested estimators are established. The application of the proposed methods to simulated and real data sets produces the favorable performance of the suggested regression shrinkage methods without the need for a grid search of the entire parameter space.
AB - One benefit of the bias-variance tradeoff is that regression estimators do not have to be strictly unbiased. However, to take full advantage of allowing bias, shrinkage regression estimators require that the appropriate level of bias is chosen carefully. Because the conventional grid search for the shrinkage parameters requires heavy computation, it is practically difficult to incorporate more than two shrinkage parameters. In this paper, we propose a class of shrinkage regression estimators which differently shrink each regression parameter. For this purpose, we set the number of shrinkage parameters to be the same as the number of regression coefficients. The ideal shrinkage for each parameter is suggested, meaning that a burdensome tuning process is not required for each parameter. The (Formula presented.) -consistency and oracle property of the suggested estimators are established. The application of the proposed methods to simulated and real data sets produces the favorable performance of the suggested regression shrinkage methods without the need for a grid search of the entire parameter space.
KW - Bias-variance tradeoff
KW - oracle property
KW - shrinkage estimator
KW - sparsity
KW - tuning parameter
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U2 - 10.1080/03610926.2019.1602649
DO - 10.1080/03610926.2019.1602649
M3 - Article
AN - SCOPUS:85065087115
SN - 0361-0926
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
ER -