Regularization and variable selection with triple shrinkage in linear regression: a generalization of lasso

Abstract

We propose a new shrinkage and variable selection method in linear regression, which is based on triple shrinkage on the regression coefficients. The new estimation method contains the ridge, lasso and elastic net as special cases. The term based on the shrunken estimator in the new method can provide estimates with a smaller length depending on the size of a new tuning parameter compared to the elastic net, maintaining the variable selection feature in the case of multicollinearity. The new estimator has the property of the grouping effect similar to that of the elastic net. The well-known coordinate descent algorithm is used to compute the coefficient path of the new estimator, efficiently. We conduct real data analysis and simulation studies to compare the new estimator with several methods including the lasso and elastic net.