Circular neighbor-balanced designs using cyclic shifts.

*(English)*Zbl 1177.05019Summary: In agriculture experiments, the response on a given plot may be affected by the treatments on neighboring plots as well as by the treatments applied to that plot. In this paper we consider such type of situations and construct circular neighbor-balanced designs (CNBDs) by the method of cyclic shifts or sets of shifts. An important feature of this method is that the properties of a design can be easily obtained from the sets of shifts instead of constructing the actual blocks of the design. That is, the off-diagonal elements of the concurrence matrix can be easily obtained from the sets of shifts. Since the suggested designs are circular, balanced and binary, so they are universally optimal.

##### MSC:

05B05 | Combinatorial aspects of block designs |

62K05 | Optimal statistical designs |

62K10 | Statistical block designs |

##### Keywords:

A-optimal; circular design; cyclic shifts; treatment balanced designs; universally optimal designs; plots; circular neigbour-balanced designs; CNBD; concurrence matrix
PDF
BibTeX
XML
Cite

\textit{I. Iqbal} et al., Sci. China, Ser. A 52, No. 10, 2243--2256 (2009; Zbl 1177.05019)

Full Text:
DOI

##### References:

[1] | Ai M Y, Ge G, Chan L Y. Circular neighbor-balanced designs universally optimal for total effects. Sci China Ser A, 50: 821–828 (2007) · Zbl 1121.62070 · doi:10.1007/s11425-007-0035-2 |

[2] | John J A. Cyclic Designs. London: Chapman and Hall, 1987 · Zbl 0731.05001 |

[3] | Rees H D. Some designs of use in Serology. Biometrics, 23: 779–791 (1967) · doi:10.2307/2528428 |

[4] | Lawless J F. A note on certain types of BIBDs balanced for residual effects. Ann Math Statist, 42: 1439–1441 (1971) · Zbl 0237.05006 · doi:10.1214/aoms/1177693256 |

[5] | Hawang F K. Construction of some classes of neighbor designs. Ann Statist, 1: 786–790 (1973) · Zbl 0262.62038 · doi:10.1214/aos/1176342476 |

[6] | Das A D, Saha G M. On the construction of neighbor designs. Calcutta Statist Assoc Bull, 25: 151–164 (1976) · Zbl 0382.62062 |

[7] | Dey A, Chakravarty R. On the construction of some classes of neighbor designs. J Indian Soc Agri Statist, 29: 97–104 (1977) |

[8] | Hawang F K, Lin S. Neighbor designs. J Combin Theory Ser A, 23: 302–313 (1977) · Zbl 0405.05017 · doi:10.1016/0097-3165(77)90021-8 |

[9] | Kageyama S. A note on designs in Serology. J Japan Statist Soc, 9: 37–40 (1979) |

[10] | Nair C R. A note on construction of neighbor designs. J Indian Soc Agri Statist, 32: 129–132 (1980) |

[11] | Chandak M L, On the construction of some families of neighbor designs. J Indian Statist Assoc, 19: 1–7 (1981) · Zbl 0503.62075 |

[12] | Street A P, A survey of neighbor designs. Congr Numer, 34: 119–155 (1982) |

[13] | Misra B L, Baghwandas, Nutan S M. Families of neighbor designs and their analysis. Comm Statist Simul comput, 20: 427–436 (1991) · Zbl 0850.62613 · doi:10.1080/03610919108812963 |

[14] | Azaiz J M, Bailey R A, Monod H. A catalogue of efficient neighbor-designs with border plots. Biometrics, 49: 1252–1261 (1993) · doi:10.2307/2532269 |

[15] | Preece D A. Balanced Ouchterlony neighbor designs and quasi-Rees neighbor designs. J Combin Math Combin Comput, 15: 197–219 (1994) · Zbl 0806.05022 |

[16] | Bailey R A, Ollis M A, Preece D A. Round-dance neighbor designs from terraces. Discrete Math, 266: 69–86 (2003) · Zbl 1025.05010 · doi:10.1016/S0012-365X(02)00799-9 |

[17] | Bailey R A, Druilhet P. Optimality of neighbor-balanced designs for total effects. Ann Statist, 32: 1650–1661 (2004) · Zbl 1045.62074 · doi:10.1214/009053604000000481 |

[18] | Filipiak K, Markiewicz A. Optimality and efficiency of circular neighbor-balanced designs for correlated observations. Metrika, 61: 17–27 (2005) · Zbl 1062.62136 · doi:10.1007/s001840400321 |

[19] | Druilhet P. Optimality of neighbor-balanced designs. J Statist Plann Inference, 81: 141–152 (1999) · Zbl 0939.62076 · doi:10.1016/S0378-3758(99)00004-X |

[20] | Iqbal I, Tahir M H. Construction of test-control treatment block designs when k > v. Aligarh J Statist, 28: 55–73 (2008). · Zbl 1305.62286 |

[21] | Iqbal I, Tahir M H. Circular strongly balanced repeated measurements designs. Comm Statist-Theory Methods, 38(20): (2009) DOI: 10-1080/03610920802642566 · Zbl 1285.05019 |

[22] | Iqbal I, Tahir M H, Akhtar M, et al. Generalized polygonal designs with block size 3 and \(\lambda\) = 1. J Statist Plann Inference, 139: 3200–3219 (2009) · Zbl 1167.05008 · doi:10.1016/j.jspi.2009.02.018 |

[23] | Iqbal I. Construction of experimental designs using cyclic shifts. Ph D. Thesis. UK: University of Kent at Canterbury, 1991 |

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.