Sequential Lasso for feature selection with ultra-high dimensional feature space

We propose a novel approach, Sequential Lasso, for feature selection in linear regression models with ultra-high dimensional feature spaces. We investigate in this article the asymptotic properties of Sequential Lasso and establish its selection consistency. Like other sequential methods, the implementation of Sequential Lasso is not limited by the dimensionality of the feature space. It has advantages over other sequential methods. The simulation studies comparing Sequential Lasso with other sequential methods are reported.