Nonconcave penalized composite conditional likelihood estimation of sparse Ising models

Rejoinder : One - Step Sparse Estimates in Nonconcave Penalized Likelihood Models

We would like to take this opportunity to thank the discussants for their thoughtful comments and encouragements on our work. The discussants raised a number of issues from theoretical as well as computational perspectives. Our rejoinder will try to provide some insights into these issues and address specific questions asked by the discussants. Most traditional variable selection criteria, such...

Supplementary materials for “Non-concave Penalized Composite Likelihood Estimation of Sparse Ising Models”

One-step Sparse Estimates in Nonconcave Penalized Likelihood Models.

Fan & Li (2001) propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function is computationally challenging, because the objective function is nondifferentiable and nonconcave. In this article we propose a new unified algorithm ...

Discussion of “ One - step sparse estimates in nonconcave penalized likelihood models ( H . Zou and R . Li ) ”

Hui Zou and Runze Li ought to be congratulated for their nice and interesting work which presents a variety of ideas and insights in statistical methodology, computing and asymptotics. We agree with them that oneor even multi-step (or -stage) procedures are currently among the best for analyzing complex data-sets. The focus of our discussion is mainly on high-dimensional problems where p n: we ...

Rejoinder: One-step Sparse Estimates in Nonconcave Penalized Likelihood Models By

Most traditional variable selection criteria, such as the AIC and the BIC, are (or are asymptotically equivalent to) the penalized likelihood with the L0 penalty, namely, pλ(|β|) = 2λI (|β| = 0), and with appropriate values of λ (Fan and Li [7]). In general, the optimization of the L0-penalized likelihood function via exhaustive search over all subset models is an NP-hard computational problem....