Asymptotics of adaptive design with two alternating generating matrices

In the application of generalized Pólya urn (GPU) model to designs of clinical trials, in contrast to the classical homogeneous models, it is more realistic to assume nonhomogeneous generating matrices. However, in literature, due to mathematical difficulties, the generating matrices are either assumed to be homogeneous or asymptotically homogeneous (see Bai and Hu, 1999). In the present paper, we consider a new model which uses two alternating generating matrices. The theoretical results show that the asymptotics still hold in this nonhomogeneous case. Moreover, the simulation results also support the theoretical conclusions. Furthermore, this model provides a starting point for the future study of adaptive designs with non-convergent generating matrices.