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Circular binary block second- and higher-order neighbor designs. (English) Zbl 1169.05009
A neighbor design with \(v\) treatments is a collection of circular blocks of constant size, \(k\), such that any 2 treatments appear in a block equally often as neighbors. They can be used for estimating treatment effects and nearest neighbor effects. If any 2 treatments also occur together equally often and 2nd order neighbors, 3rd order neighbors …\(p\)th order neighbors, the design is called a \(p\)th order neighbor design. The authors provide new examples of 2nd, 3rd and 4th order neighbor designs, mostly with \(k\) in \(\{v,v-1,(v-1)/2\}\), that are either cyclic or 1-rotational. Some statistical models applicable to these designs are also given.

05B05 Combinatorial aspects of block designs
62K10 Statistical block designs
62K05 Optimal statistical designs
Full Text: DOI
[1] DOI: 10.2307/2532269 · doi:10.2307/2532269
[2] DOI: 10.1214/009053604000000481 · Zbl 1045.62074 · doi:10.1214/009053604000000481
[3] DOI: 10.1016/S0378-3758(99)00004-X · Zbl 0939.62076 · doi:10.1016/S0378-3758(99)00004-X
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[8] DOI: 10.2307/2528428 · doi:10.2307/2528428
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