Larry Brown’s Work on Admissibility

Abstract

Many papers in the early part of Brown’s career focused on the admissibility or otherwise of estimators of a vector parameter. He established that inadmissibility of invariant estimators in three and higher dimensions is a general phenomenon, and found deep and beautiful connections between admissibility and other areas of mathematics. This review touches on several of his major contributions, with a focus on his celebrated 1971 paper connecting admissibility, recurrence and elliptic partial differential equations.