Abstract
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.
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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)
John J A. Cyclic Designs. London: Chapman and Hall, 1987
Rees H D. Some designs of use in Serology. Biometrics, 23: 779–791 (1967)
Lawless J F. A note on certain types of BIBDs balanced for residual effects. Ann Math Statist, 42: 1439–1441 (1971)
Hawang F K. Construction of some classes of neighbor designs. Ann Statist, 1: 786–790 (1973)
Das A D, Saha G M. On the construction of neighbor designs. Calcutta Statist Assoc Bull, 25: 151–164 (1976)
Dey A, Chakravarty R. On the construction of some classes of neighbor designs. J Indian Soc Agri Statist, 29: 97–104 (1977)
Hawang F K, Lin S. Neighbor designs. J Combin Theory Ser A, 23: 302–313 (1977)
Kageyama S. A note on designs in Serology. J Japan Statist Soc, 9: 37–40 (1979)
Nair C R. A note on construction of neighbor designs. J Indian Soc Agri Statist, 32: 129–132 (1980)
Chandak M L, On the construction of some families of neighbor designs. J Indian Statist Assoc, 19: 1–7 (1981)
Street A P, A survey of neighbor designs. Congr Numer, 34: 119–155 (1982)
Misra B L, Baghwandas, Nutan S M. Families of neighbor designs and their analysis. Comm Statist Simul comput, 20: 427–436 (1991)
Azaiz J M, Bailey R A, Monod H. A catalogue of efficient neighbor-designs with border plots. Biometrics, 49: 1252–1261 (1993)
Preece D A. Balanced Ouchterlony neighbor designs and quasi-Rees neighbor designs. J Combin Math Combin Comput, 15: 197–219 (1994)
Bailey R A, Ollis M A, Preece D A. Round-dance neighbor designs from terraces. Discrete Math, 266: 69–86 (2003)
Bailey R A, Druilhet P. Optimality of neighbor-balanced designs for total effects. Ann Statist, 32: 1650–1661 (2004)
Filipiak K, Markiewicz A. Optimality and efficiency of circular neighbor-balanced designs for correlated observations. Metrika, 61: 17–27 (2005)
Druilhet P. Optimality of neighbor-balanced designs. J Statist Plann Inference, 81: 141–152 (1999)
Iqbal I, Tahir M H. Construction of test-control treatment block designs when k > v. Aligarh J Statist, 28: 55–73 (2008).
Iqbal I, Tahir M H. Circular strongly balanced repeated measurements designs. Comm Statist-Theory Methods, 38(20): (2009) DOI: 10-1080/03610920802642566
Iqbal I, Tahir M H, Akhtar M, et al. Generalized polygonal designs with block size 3 and λ = 1. J Statist Plann Inference, 139: 3200–3219 (2009)
Iqbal I. Construction of experimental designs using cyclic shifts. Ph D. Thesis. UK: University of Kent at Canterbury, 1991
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Iqbal, I., Tahir, M.H. & Ghazali, S.S.A. Circular neighbor-balanced designs using cyclic shifts. Sci. China Ser. A-Math. 52, 2243–2256 (2009). https://doi.org/10.1007/s11425-009-0063-1
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DOI: https://doi.org/10.1007/s11425-009-0063-1