# zbMATH — the first resource for mathematics

Construction of neighbor balanced block designs. (English) Zbl 1211.62132
Summary: Neighbor designs with complete blocks for all odd $$\nu$$ (number of treatments) were generated by D. H. Rees [Biometrics 23, 779–791 (1967)]. Since then this is a well investigated field. Here some new algorithms have been developed to generate (a) complete block neighbor designs for $$\nu=4s$$; $$s$$ is a natural number, (b) neighbor balanced designs for $$k=\nu-1$$ when $$\nu$$ is odd, (c) neighbor balanced designs for $$k=\nu-1$$ when $$\nu=4s$$ and (d) all order neighbor balanced complete block designs for $$\nu$$ an odd prime, in the minimum number of blocks when right and left neighbor effects are equal. In all cases the blocks are circular and well separated. A catalogue of complete block neighbor designs for $$\nu=4s$$ generated through algorithm given in part (a) is also presented.

##### MSC:
 62K10 Statistical block designs 65C60 Computational problems in statistics (MSC2010)
Full Text:
##### References:
 [1] Azais J. M., Biometrics 49 (4) pp 1252– (1993) · doi:10.2307/2532269 [2] Bailey R. A., Annals of Statistics 32 (4) pp 1650– (2004) · Zbl 1045.62074 · doi:10.1214/009053604000000481 [3] Das A. D., Calcutta Statist. Assoc. Bull. 25 pp 151– (1976) [4] Druilhet P., Journal of Statistical Planning and Inference 81 pp 141– (1999) · Zbl 0939.62076 · doi:10.1016/S0378-3758(99)00004-X [5] Filipiak K., Metrika 61 pp 17– (2005) · Zbl 1062.62136 · doi:10.1007/s001840400321 [6] Filipiak K., Listy Biometryczne &#num;8211; Biometrical Letters 42 (2) pp 133– (2005) [7] Hwang F. K., Annals of Statistics 1 (4) pp 786– (1973) · Zbl 0262.62038 · doi:10.1214/aos/1176342476 [8] Hwang F. K., Journal of Combinatoric Theory A 23 pp 302– (1977) · Zbl 0405.05017 · doi:10.1016/0097-3165(77)90021-8 [9] Iqbal I., Journal of Research (Science), BZU, Multan, Pakistan 17 (3) pp 191– (2006) [10] Jacroux M., The Indian Journal of Statistics 60 (3) pp 488– (1998) [11] Kageyama S., Journal of Japan Statistical Society 9 pp 37– (1979) [12] Lawless J. F., Annals of Mathematical Statistics 42 pp 1439– (1971) · Zbl 0237.05006 · doi:10.1214/aoms/1177693256 [13] Misra B. L., Commun. Statist. Simul. Comput. 20 (2) pp 427– (1991) · Zbl 0850.62613 · doi:10.1080/03610919108812963 [14] Muller W. G., Biometrika 90 (2) pp 423– (2003) · Zbl 1035.62077 · doi:10.1093/biomet/90.2.423 [15] Mingyao Ai, Journal of Science in China Series A: Mathematics 50 pp 821– (2007) · Zbl 1121.62070 · doi:10.1007/s11425-007-0035-2 [16] Nutan S. M., Construction of neighbor designs with V = 2m (2004) [17] Nutan S. M., Journal of Statistical Planning and Inference 137 pp 1681– (2007) · Zbl 1110.62096 · doi:10.1016/j.jspi.2006.09.017 [18] Preece D. A., J. Combin. Math. Combin. Comput. 15 pp 197– (1994) [19] Rees D. H., Biometrics 23 pp 779– (1967) · 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.