On the speed of convergence of some urn designs for the balanced allocation of two treatments |
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Authors: | Alessandro Baldi Antognini |
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Institution: | (1) Department of Statistical Sciences, , Via Belle Arti 41, 40126 Bologna, Italy |
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Abstract: | The present paper deals with sequential urn designs for the balanced allocation of two treatments.Wei (1977, 1978b) was among
the first authors to suggest an algorithm based on the probabilistic properties of the generalized Friedman urn and recently
Chen (2000) has suggested the Ehrenfest design, namely a sequential procedure based on the Ehrenfest urn process. Some extensions
of these algorithms are discussed: in particular we focus on a generalization of Chen's procedure, called the Ehrenfest-type
urn designs, recently introduced by Baldi Antognini (2004). By analyzing some convergence properties of the Ehrenfest process,
we show that for an Ehrenfest-type urn it is possible to evaluate the variance of the design at each step and analyze the
convergence to balance. Furthermore, the generalized Friedman urn and the Ehrenfest-type procedures are compared in terms
of speed of convergence. The Ehrenfest design proposed by Chen converges to balance faster than the other urn procedures. |
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Keywords: | Sequential design Urn models Ehrenfest process Markov chains Biased coin design |
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