×

zbMATH — the first resource for mathematics

Circular first- and second-order balanced repeated measurements designs. (English) Zbl 1227.05076
Summary: V. K. Sharma [Can. J. Stat. 5, 121–132 (1977; Zbl 0382.62067)] and M. L. Aggarwal, L.-Y. Deng and M. K. Jha [Stat. Probab. Lett. 76, No. 6, 597–600 (2006; Zbl 1086.62081)] considered non circular construction of first- and second-order balanced repeated measurements designs. V. K. Sharma, C. Varghese and S. Jaggi [J. Appl. Statist. 5, 153–162 (2002)] constructed circular first- and second-order balanced repeated measurements designs only for a class with parameters \((v, p = 3n, n = v^{2})\) and also showed its universal optimality. In this article, we consider circular construction of first- and second-order balanced repeated measurements designs and strongly balanced repeated measurements designs by using the method of cyclic shifts. Some new circular designs with parameters \((v, p, n)\) for cases \(p = v, p < v\) and \(p > v\) are given.

MSC:
05B05 Combinatorial aspects of block designs
62K05 Optimal statistical designs
62K10 Statistical block designs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1093/biomet/70.1.199 · Zbl 0502.62068 · doi:10.1093/biomet/70.1.199
[2] DOI: 10.1016/0167-7152(88)90048-X · Zbl 0665.62078 · doi:10.1016/0167-7152(88)90048-X
[3] DOI: 10.1016/0167-7152(92)90008-S · Zbl 0708.62063 · doi:10.1016/0167-7152(92)90008-S
[4] DOI: 10.1080/03610929008830426 · Zbl 0728.62071 · doi:10.1080/03610929008830426
[5] DOI: 10.1016/j.spl.2005.09.004 · Zbl 1086.62081 · doi:10.1016/j.spl.2005.09.004
[6] DOI: 10.1016/0378-3758(82)90084-2 · Zbl 0486.62074 · doi:10.1016/0378-3758(82)90084-2
[7] DOI: 10.1214/aos/1176345200 · Zbl 0461.62064 · doi:10.1214/aos/1176345200
[8] DOI: 10.2307/2983686 · doi:10.2307/2983686
[9] DOI: 10.3168/jds.S0022-0302(41)95480-2 · doi:10.3168/jds.S0022-0302(41)95480-2
[10] DOI: 10.1093/biomet/56.2.283 · Zbl 0179.23803 · doi:10.1093/biomet/56.2.283
[11] Dey A., Sankhya 45 pp 233– (1983)
[12] DOI: 10.1016/S0378-3758(00)00295-0 · Zbl 0974.62056 · doi:10.1016/S0378-3758(00)00295-0
[13] DOI: 10.1098/rspb.1956.0017 · doi:10.1098/rspb.1956.0017
[14] DOI: 10.1080/10543409808835233 · Zbl 0913.62103 · doi:10.1080/10543409808835233
[15] DOI: 10.2307/2528104 · doi:10.2307/2528104
[16] Hedayat A. S., Bull. Int. Statist. Inst. 1 pp 591– (1981)
[17] Hedayat A. S., A Survey of Statistical Design and Linear Models pp 229– (1975)
[18] DOI: 10.1214/aos/1176344206 · Zbl 0395.62056 · doi:10.1214/aos/1176344206
[19] DOI: 10.1214/aos/1056562469 · Zbl 1028.62060 · doi:10.1214/aos/1056562469
[20] DOI: 10.1016/0378-3758(94)90190-2 · Zbl 0803.62072 · doi:10.1016/0378-3758(94)90190-2
[21] DOI: 10.1080/03610920802642566 · Zbl 1285.05019 · doi:10.1080/03610920802642566
[22] Jones B., Design and Analysis of Cross-Over Trials (1989) · Zbl 0729.62068
[23] Keppel G., Design and Analysis: A Researcher’s Handbook (1973)
[24] DOI: 10.1214/aos/1176346717 · Zbl 0544.62068 · doi:10.1214/aos/1176346717
[25] DOI: 10.1080/03610928408828850 · Zbl 0565.62048 · doi:10.1080/03610928408828850
[26] DOI: 10.1080/03610928008828004 · Zbl 0457.62061 · doi:10.1080/03610928008828004
[27] Majumdar D., Statistica Sinica 18 pp 235– (2008)
[28] DOI: 10.1016/0378-3758(94)90191-0 · Zbl 0825.62649 · doi:10.1016/0378-3758(94)90191-0
[29] DOI: 10.1080/00401706.1974.10489143 · doi:10.1080/00401706.1974.10489143
[30] DOI: 10.1016/0378-3758(88)90041-9 · Zbl 0642.62043 · doi:10.1016/0378-3758(88)90041-9
[31] DOI: 10.1016/0378-3758(87)90102-9 · Zbl 0624.62077 · doi:10.1016/0378-3758(87)90102-9
[32] Senn S. J., Cross-Over Trials in Clinical Research (1993)
[33] DOI: 10.1016/S0378-3758(00)00318-9 · Zbl 0976.62106 · doi:10.1016/S0378-3758(00)00318-9
[34] DOI: 10.2307/3315089 · Zbl 0382.62067 · doi:10.2307/3315089
[35] Sharma V. K., Metron 60 pp 153– (2002)
[36] DOI: 10.1080/0266476032000075958 · Zbl 1121.62485 · doi:10.1080/0266476032000075958
[37] DOI: 10.1186/1471-2288-3-22 · doi:10.1186/1471-2288-3-22
[38] Williams E. R., Austal. J. Sci. Res. 2 pp 149– (1949)
[39] Williams E. R., Austal. J. Sci. Res. 3 pp 351– (1950)
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.