Self-adaptive Lasso and its Bayesian Estimation

In this paper, we proposed a self-adaptive lasso method for variable selection in regression problems. Unlike the popular lasso method, the proposed method introduces a specific tuning parameter for each regression coefficient. We modeled self-adaptive lasso in a Bayesian framework and developed an efficient Gibbs sampling algorithm to automatically select these tuning parameters and estimate the parameters. This algorithm also brings in some convenience for conducting statistical inference for selected variables. Several synthetic and real examples in this paper demonstrate flexibility of the tuning parameters enhance the performance of self-adaptive lasso in terms of both prediction and variable selection. Finally, we also extend the self-adaptive lasso to account for elastic net and fused lasso.