Identification of universally optimal circular designs for the interference model

摘 要：
Many applications of block designs exhibit neighbor and edge effects. A popular remedy is to use the circular design coupled with the interference model. The search for optimal or efficient designs has been intensively studied in recent years. The circular neighbor balanced designs at distances 1 and 2 (CNBD2), including orthogonal array of type I of strength 2, are the two major designs proposed in literature for the purpose of estimating the direct treatment effects. They are showed to be optimal within some reasonable subclasses of designs. By using benchmark designs in approximate design theory, we show that CNBD2 is highly efficient among all possible designs when the error terms are homoscedastic and uncorrelated. However, when the error terms are correlated, these designs will be outperformed significantly by other designs. Note that CNBD2 fall into the special catalog of pseudo symmetric designs, and they only exist when the number of treatments is larger than the block size and the number of blocks is multiple of some constants. In this paper, we elaborate equivalent conditions for any design, pseudo symmetric or not, to be universally optimal for any size of experiment and any covariance structure of the error terms. This result is novel for circular designs and sheds light on other similar models in the search for optimal or efficient asymmetric designs. This is a collaboration work with Mingyao Ai and Kang Li from Peking University.
个人简介：
Wei Zheng, Ph.D., joins the Department of Mathematical Sciences at IUPUI as an assistant professor after completing his Ph.D. in statistics at the University of Illinois, Chicago (UIC).
Zheng’s research has focused on identifying optimal or efficient crossover designs, which are widely used in clinical trials, pharmaceutical studies, psychological experiments, agriculture field trails, animal feeding experiments and many other branches of science. His interest falls in optimal designs for both parameter estimation and hypothesis testing for different types of models both linear and nonlinear.
Zheng’s was working on the limiting distributions of sample covariance of a long memory time series. He will continue to be interested in asymptotic theory for statistics from dependent observations. Using the expertise in both design and time series, he would like to explore areas of adaptive designs where optimal designs depend on the unknown parameter to be estimated, as well as spatio-temporal modeling in topics of image processing, environmental and geographical sciences in which the design aspect has merely been touched.
 Dr. Zheng received his B.S. in mathematics specialized in statistics from Zhejiang University in China.

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 华南统计科学研究中心
 2016/7/4