×

zbMATH — the first resource for mathematics

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.

MSC:
05B05 Combinatorial aspects of block designs
62K10 Statistical block designs
62K05 Optimal statistical designs
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
[4] Filipiak K., Listy Biometryczne & # 8211; Biometrical Letters 42 (2) pp 133– (2005)
[5] Ipinyomi , R. A. ( 1985 ). Equineighbored Experimental Designs . PhD thesis , UK : University of Southampton .
[6] Iqbal I., Journal of Research (Science) 17 (3) pp 191– (2006)
[7] DOI: 10.1007/s11425-007-0035-2 · Zbl 1121.62070 · doi:10.1007/s11425-007-0035-2
[8] DOI: 10.2307/2528428 · doi:10.2307/2528428
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.