TY - JOUR
T1 - On grouping effect of elastic net
AU - Zhou, Ding-Xuan
PY - 2013/9
Y1 - 2013/9
N2 - 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. © 2013 Elsevier B.V.
AB - 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. © 2013 Elsevier B.V.
KW - Approximation error
KW - Elastic net
KW - Grouping effect
KW - Reproducing kernel Hilbert space
KW - Variable selection
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84879166428&origin=recordpage
U2 - 10.1016/j.spl.2013.05.014
DO - 10.1016/j.spl.2013.05.014
M3 - 21_Publication in refereed journal
VL - 83
SP - 2108
EP - 2112
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 9
ER -