Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models

TL;DR

This paper responds to discussions on one-step sparse estimation methods in nonconcave penalized likelihood models, addressing theoretical and computational issues raised by peers.

Contribution

It offers clarifications and insights into the theoretical and computational aspects of one-step sparse estimation in nonconcave penalized likelihood models.

Findings

Addresses theoretical concerns about estimation consistency.

Provides computational strategies for efficient implementation.

Clarifies the advantages of one-step estimation methods.

Abstract

We would like to take this opportunity to thank the discussants for their thoughtful comments and encouragements on our work [arXiv:0808.1012]. 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.