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1. Introduction. Compound decision theory and empirical Bayes methodology , acclaimed as " two breakthroughs " by Neyman (1962), are the most important contributions of Herbert Robbins to statistics. The purpose of this paper is to provide a brief description of his work in these two intimately connected fields, its impact and a number of important related(More)
Points P 1 ,. .. , P n in the unit square define a convex n-chain if they are below y = x and, together with P 0 = (0, 0) and P n+1 = (1, 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established(More)
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