Various adaptive designs have been proposed and applied to clinical trials, bio assay, psychophysics, etc.Adaptive designs are also useful in high cost engineering trials.More and more people have been paying attentio...Various adaptive designs have been proposed and applied to clinical trials, bio assay, psychophysics, etc.Adaptive designs are also useful in high cost engineering trials.More and more people have been paying attention to these design methods. This paper introduces several broad families of designs, such as the play-the-winner rule, randomized play-the-winner rule and its generalization to the multi-arm case, doubly biased coin adaptive design, Markov chain model.展开更多
The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that ...The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of a stochastic differential equation.This Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical inferences.As an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.展开更多
文摘Various adaptive designs have been proposed and applied to clinical trials, bio assay, psychophysics, etc.Adaptive designs are also useful in high cost engineering trials.More and more people have been paying attention to these design methods. This paper introduces several broad families of designs, such as the play-the-winner rule, randomized play-the-winner rule and its generalization to the multi-arm case, doubly biased coin adaptive design, Markov chain model.
基金supported by National Natural Science Foundation of China (Grant No. 10771192)National Science Foundation of USA (Grant No. DMS-0349048)
文摘The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of a stochastic differential equation.This Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical inferences.As an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.
