Discussion of 'The Contributions of Robert A. Wijsman to Sequential Analysis' by Adam T. Martinsek

摘要

I am pleased to have this opportunity to add a few remarks about Bob Wijsman and his important contributions to sequential analysis. Adam Martinsek's paper does an excellent job, in capturing both the essence of Bob's approach to his work and the clarity, precision, and thoroughness inevitably found in Bob's finished products, his publications. My interactions with Bob were primarily with regard to our joint paper on sufficiency and invariance, published in 1965 after several years of refinements and extensions—all by mail. The history of that collaboration appears in the publication. Don Burkholder, I, and Jayanta Ghosh each, in turn, independently rediscovered a result developed earlier by Charles Stein. Don chatted with Bob about this, and Bob pursued it with his usual preciseness, depth, and thoroughness. The Annals' editor put us in touch, but Don dropped out, as his interests had turned elsewhere. My first submission had not recognized the need for distinguishing between invariance and almost invariance, but Bob soon set me straight. We corresponded for some time about a joint manuscript, and soon realized that a two-part paper was the best solution: a precise and careful mathematical development, under Bob's direction, and a chatty version including the basic ideas and its applications to sequential analysis, under my direction. Before we could complete these tasks, Jayanta Ghosh submitted a paper to the Annals based on his dissertation, with a great deal of overlap but also some new material, especially on transitivity, and so he joined in. This joint endeavor was a delightful experience; I only wish we had found other joint activities to pursue.