Once a month during the academic year, the statistics faculty select a paper for our students to read and discuss. Papers are selected based on their impact or historical value, or because they contain useful techniques or results.
Bickel, P.J. and Li, B. (2006) Regularization in statistics. Test 15, 271–344.
Notes preparer: Kun Chen and Yuwen Gu
Regularization is frequently used in mathematics, statistics, computer science, and finance to solve ill-posed problems that could not be otherwise solved. In statistics alone, various regularization techniques have been proposed in different research directions, such as nonparametric statistics, high-dimensional statistics, and Bayesian statistics. Before this discussion paper by Bickel and Li (2006), these were just scattered results without a neat organization. Bickel and Li were among the first to bring up a conceptual framework to incorporate most statistical regularizers under the same umbrella. We will go over these regularization methods mentioned in this paper and discuss the vast new developments ever since.