Asymptotics of adaptive designs based on URN models

Abstract

In adaptive design based on urn models, it is common that the response is delayed for several stages or even does not occur at all. To avoid the waste of resources while do not lose the information, we propose a design which stops tracking a response if it does not occur within M stages and establish the asymptotic theorem. Moreover, we also consider possible missing data in the model.In addition, we obtain the asymptotic results for a type of adaptive design that uses two alternating generating matrices. In this design, the urn model is non-convergent.Finally, we consider the asymptotics of a linear combination of Yn and Nn on I?, where I? consists of s blocks and each block is made up of the vectors in the basis of the cyclic space of H-I>iI for each I>i. In particular, in the case that I?=1/2, we give the exact expression of each term in the variance-covariance matrix.