Adaptive Elastic Net: An Improvement of Elastic Net

Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not capture any grouping effect and secondly in some situations lasso solutions are inconsistent. To overcome inconsistency recently adaptive lasso was proposed where adaptive weights are used for penalizing different coefficients. Adaptive lasso enjoys oracle properties. Also recently a doubly regularized technique namely elastic net was proposed which encourages grouping effect i.e. either selection or omission of the correlated variable together and is particularly useful when the number of covariates (p) is much larger than the number of observations (n). However even for usual p < n case it does not deemed to be an oracle procedure. In this paper we propose a new version of the elastic net called adaptive elastic net which inherits some of the desirable properties of the adaptive lasso and elastic net. We explicitly prove its oracle properties for p < n case. An efficient algorithm was proposed in the line of LARS-EN which is then illustrated with simulated as well as real life data examples.