Asymptotic statistical properties of a response adaptive design based on a two colours urn model

We present a new response adaptive design, described in terms of a two colors urn model with non-negative and diagonal reinforcement matrix. The model consists in a modification of the Randomly Reinforced Urn design aiming to target any prespecified asymptotic allocation. Besides the main convergence theorem, we present further asymptotic results concerning the asymptotic behaviour of different quantities related to the urn process. We introduce suitable statistics to test the hypothesis on treatment’s differences and we study the statistical proprieties of these inferential procedures.