Circular binary block second- and higher-order neighbor designs. (English) Zbl 1169.05009

Akhtar, Munir; Ahmed, Rashid

Commun. Stat., Simulation Comput. 38, No. 4, 821-828 (2009).

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.

Reviewer: Julian Abel (Sydney)

MSC:

05B05	Combinatorial aspects of block designs
62K10	Statistical block designs
62K05	Optimal statistical designs

Keywords:

fourth-order neighbor design; third-order neighbor design; second-order neighbor design; universally optimal design

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