Estimation after adaptive allocation

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An adaptive randomized design with application to estimation (2001, methodology): “Early examples of such designs include a design for the Behrens-Fisher problem, in Robbins et al. (1967), and a design to minimize the expected number of patients allocated to the inferior treatment in Robbins & Siegmund (1974). These early designs are deterministic in the sense that the population ”
Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn (2009, background): “In this section, we show that these estimators, appropriately standardized, are jointly asymptotically normal, despite the randomness of NB(n) and NW (n), their dependence, and the fact that they don’t satisfy the classical assumption, as also is required in [21], Theorem 3.”
Asymptotic theorems of sequential estimation-adjusted urn models (2006, unknown): “And then by Lemma 5.1, we conclude that Yn − nv= o(n) + n−1∑ m=1 o(m) m+ 1 (n/m)λ logν−1(n/m) = o(n) a.s., that is, Yn n → v a.s. Finally, from (5.7) it follows that Nn − nv= o(n) + n−1∑ m=0 o(m) m+ 1 + n−1∑ m=0 ( Ym |Ym| − v ) o(1) = o(n) a.s.”
Asymptotically best response-adaptive randomization procedures (2006, methodology): “When = 0, we have a procedure explored by Melfi and Page (1998, 2000) with limiting Neyman allocation, and they discovered that this procedure was highly variable.”