Revisiting LCME Empirical Bayes Shrinkage: A Finite Sample Risk Analysis of Tail Accumulation and Thresholding

This record contains the manuscript of “Revisiting LCME Empirical Bayes Shrinkage: A Finite Sample Risk Analysis of Tail Accumulation and Thresholding,” together with the LaTeX source, Python code used for the numerical illustrations, and the complete simulation outputs. The manuscript develops finite sample and asymptotic risk results for least concave majorant empirical Bayes shrinkage in the Gaussian sequence model. Topics include pure noise tail accumulation, hard threshold risk identities, polynomial and exponential prior variance decay, localization of the LCME crossing, multiplicative and shape misspecification, finite horizon smooth LCME, conservative noise estimation, and numerical illustrations. The simulation archive contains the figure files in PDF and PNG format, the underlying CSV results, and summary outputs. The Python script reproduces the numerical experiments reported in the manuscript.