摘要
In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.
In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighborbalanced at distances up to γ ? k ? 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up to γ among the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k ? 1 are provided.
基金
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10671007,10471127)
Zhejiang Provincial Natural Science Foundation of China (Grant No. R604001)
the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China and a CERG grant from Research Grants Council of Hong Kong
