A note on adaptive Lp regularization

In this paper, the adaptive L_p regularization is proposed for parameter estimation and variable selection. In particular, we focus on the (0 <; p <; 1) case when the adaptive L_p regularizer has a nonconvex penalty. Besides some traditional properties for penalized linear regression model, such as unbiasedness and sparsity, we have shown that the adaptive L_p regularization also enjoy the oracle property. A modified iterative algorithm is utilized to solve the adaptive L_p. By comparing with ordinary least square, adaptive lasso and L_p, the numerical results show that the adaptive L_p is more accurate and sparse.