Some Asymptotic Properties Of Randomized Design Based On Two Treatments

The paper studies some statistical properties about two kinds of randomized designs (urn models and biased coin designs). The focus of the paper is mainly about the mathmatical charateristics and large sample asympototic properties of randomized models based on two treatments. Through exploring theoretical properties of these models, we compare the speed of convergence of some designs for balanced allocation of two treatments, adaptive randomized urn models, generalized Friedman urn design, generalized Polya urn model, and biased coin design. Furthermore, we consider some factors which affect the speed of the convergence. These theoretical results provide some criterions for choosing reasonable design in practical clinical trials.