Circular neighbor-balanced designs universally optimal for total effects

【摘要】 <正>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.更多还原

【Abstract】 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.更多还原