Estimation after adaptive allocation

In recent years a vast number of adaptive designs have been proposed, often in the context of clinical trials or industrial applications. The adjective adaptive refers to the feature that, in such designs, the current allocation may depend on data already collected. When analyzing such designs, proving consistency and asymptotic normality of estimators is of fundamental importance. For some designs, this has not yet been done. When it has, the proofs have been tailored to the particular design being analyzed, often utilizing martingale arguments. In this paper independence properties of the allocated sequence are proved and then used to provide a simple method for proving consistency and asymptotic normality of estimators for a wide class of designs. (C) 2000 Elsevier Science B.V. All rights reserved.