TypeS designs with nested rows and columns

Summary Supplemented balance in block designs with nested rows and columns is considered, under the name of typeS designs with nested rows and columns. Analysis and construction of such designs are also discussed.     

Optimal design for interacting blocks with OAVS incidence

Optimal design is studied for multiway cross classifications in which the blocking factors exhibit interaction and in which the incidence structure of the blocking factors describes an orthogonal array. Assuming the orthogonal array to be of sufficient strength (enough to allow orthogonal estimation of all of the interaction terms), easily used forms of the information matrix for treatment estimation are derived, and optimality conditions are stated. Some illustrative construction examples are given.     

Optimal extended complete block designs for dependent observations

Optimal designs under general dependence structures are usually difficult to specify theoretically or find algorithmically. However, they can sometimes be found for a specific dependence structure and a particular parameter value. In this paper, a class of generalized binary block designs with t treatments and b blocks of size k>t is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k−ht (if k > ht). For a suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. Some constructions for a universally optimal design are described. A negative dependence parameter, and some other dependence structures, are also considered.