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April 2015 Universally optimal designs for two interference models
Wei Zheng
Ann. Statist. 43(2): 501-518 (April 2015). DOI: 10.1214/14-AOS1287


A systematic study is carried out regarding universally optimal designs under the interference model, previously investigated by Kunert and Martin [Ann. Statist. 28 (2000) 1728–1742] and Kunert and Mersmann [J. Statist. Plann. Inference 141 (2011) 1623–1632]. Parallel results are also provided for the undirectional interference model, where the left and right neighbor effects are equal. It is further shown that the efficiency of any design under the latter model is at least its efficiency under the former model. Designs universally optimal for both models are also identified. Most importantly, this paper provides Kushner’s type linear equations system as a necessary and sufficient condition for a design to be universally optimal. This result is novel for models with at least two sets of treatment-related nuisance parameters, which are left and right neighbor effects here. It sheds light on other models in deriving asymmetric optimal or efficient designs.


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Wei Zheng. "Universally optimal designs for two interference models." Ann. Statist. 43 (2) 501 - 518, April 2015.


Published: April 2015
First available in Project Euclid: 24 February 2015

zbMATH: 1314.62173
MathSciNet: MR3316188
Digital Object Identifier: 10.1214/14-AOS1287

Primary: 62K05
Secondary: 62J05

Keywords: approximate design theory , Interference model , linear equations system , pseudo symmetric designs , universally optimal designs

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 2 • April 2015
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