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Circular neighbor-balanced designs universally optimal for total effects. (English) Zbl 1121.62070
Summary: In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor balanced at distances up to \(\gamma \leq k - 1\), where \(k\) is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up to \(\gamma\) among the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to \(k - 1\) are provided.

62K05 Optimal statistical designs
62K10 Statistical block designs
05B05 Combinatorial aspects of block designs
Full Text: DOI
[1] Cochran W G, Cox G M. Experimental Designs, 2nd ed. New York: John Wiley & Sons, 1957 · Zbl 0077.13205
[2] Dey A. Theory of Block Designs. New Delhi: John Wiley & Sons, 1986 · Zbl 0653.05010
[3] Hedayat A, Afsarinejad K. Repeated measurements designs II. Ann Statist, 6: 619–628 (1978) · Zbl 0395.62056 · doi:10.1214/aos/1176344206
[4] Cheng C S, Wu C F J. Balanced repeated measurements designs. Ann Statist, 8: 1272–1283 (1980) · Zbl 0461.62064 · doi:10.1214/aos/1176345200
[5] Kunert J. Optimality of balanced uniform repeated measurements designs. Ann Statist, 12: 1006–1017 (1984) · Zbl 0544.62068 · doi:10.1214/aos/1176346717
[6] Kushner H B. Optimal repeated measurements designs: The linear optimality equations. Ann Statist, 25:2328–2344 (1997) · Zbl 0894.62088 · doi:10.1214/aos/1030741075
[7] Kunert J. Design balanced for circular residual effects. Comm Statist A-Theory Methods, 13: 2665–2671 (1984) · Zbl 0565.62048 · doi:10.1080/03610928408828850
[8] Azaïs 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
[9] 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
[10] Bailey R A, Druilhet P. Optimality of neighbor-balanced designs for total effects. Ann Statist, 32(4):1650–1661 (2004) · Zbl 1045.62074 · doi:10.1214/009053604000000481
[11] Kiefer J. Construction and optimality of generalized Youden designs. In: Srivastatva J N, ed. A Survey of Statistical Design and Linear Models. Amsterdam: North-Holland, 1975, 333–353
[12] Shah K R, Sinha B K. Theory of Optimal Designs. Lecture Notes in Statist, Vol 54. New York: Springer, 1989 · Zbl 0688.62043
[13] Bennett F E. Recent progress on the existence of perfect Mendelsohn designs. J Statist Plann Inference, 94: 121–138 (2001) · Zbl 0985.05003 · doi:10.1016/S0378-3758(00)00245-7
[14] Dénes J, Keedwell A D. Latin Squares and Their Applications. New York: Academic Press, 1974 · Zbl 0283.05014
[15] Colbourn C J, Dinitz J H. CRC Handbook of Combinatorial Designs. Boca Raton: CRC Press Inc, 1996 · Zbl 0836.00010
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