Special feature: Stein estimation and statistical shrinkage methods

The twelfth special issue of the Japanese Journal of Statistics and Data Science (JJSD) focuses on statistics for shrinkage estimation.In recent years, statistical shrinkage methods have become increasingly prevalent for addressing scientific inquiries, particularly in experiments and scenarios involving inference and prediction based on large-scale data.Initially, the effectiveness of Stein-type shrinkage estimation relied on statistical decision theory and empirical Bayes inference.Present-day methodologies in shrinkage methods offer scalable inference techniques to tackle intricate problems across various domains, including the biological sciences, signal processing, economics, and finance.Despite the flourishing development of modern shrinkage methods, numerous theoretical and computational challenges persist.This special feature comprises fourteen papers aimed at showcasing recent research and reviews pertinent to Stein estimation and statistical shrinkage methods.Within these papers, readers will encounter a diverse array of theories, methodologies, and empirical analyses.The papers in the special feature are summarized as follows:The first article is "Machine learning and the James-Stein estimator" by Bradley Efron.The seminal work of James and Stein on estimating a multivariate normal mean vector made a spectacular first impression on the statistical community through its demonstration of inadmissibility of the maximum likelihood estimator.Efron points out that it continues to be influential, but not for the initial reasons.In the 1970s, Efron and Carl Morris collaborated on a series of papers where they justified the James-Stein estimator as an empirical Bayes shrinkage procedure.Furthermore, as Efron highlights, modern topics such as Benjamini and Hochberg's false discovery rate algorithm can trace their roots back to the empirical Bayes method.Tragically, Morris passed away during the publication process.