@article{055ae7d7a1704bd48ae382df80f9cd4b, title = "On grouping effect of elastic net", abstract = "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. {\textcopyright} 2013 Elsevier B.V.", keywords = "Approximation error, Elastic net, Grouping effect, Reproducing kernel Hilbert space, Variable selection", author = "Ding-Xuan Zhou", year = "2013", month = sep, doi = "10.1016/j.spl.2013.05.014", language = "English", volume = "83", pages = "2108--2112", journal = "Statistics and Probability Letters", issn = "0167-7152", publisher = "ELSEVIER SCIENCE BV", number = "9", }