Chai, Feng-Shun; Chatterjee, Kashinath; Gupta, Sudhir Generalized \(E(s^{2})\) criterion for multilevel supersaturated designs. (English) Zbl 1177.62091 Commun. Stat., Theory Methods 38, No. 20, 3725-3735 (2009). Summary: Several extensions of the popular \(E(s^{2})\) criterion of K. H. V. Booth and D. R. Cox [Technometrics 4, 489–495 (1962; Zbl 0109.12201)] to multilevel supersaturated designs have been advanced in the literature. These extensions are not unique due to different ways they measure overall non-orthogonality between all pairs of the columns of the model matrix. We exploit the connection of the \(E(s^{2})\) criterion with \(A\)- and \(D\)-optimality that naturally lends itself to a generalized criterion for the multilevel situation in a unified way. The extensions provided in the literature follow as special cases of the generalized criterion. A lower bound to the generalized criterion is derived for a wide class of designs, and a method of construction for the symmetrical case is discussed. Cited in 3 Documents MSC: 62K05 Optimal statistical designs 62K15 Factorial statistical designs Keywords:\(A\)-optimality; \(D\)-optimality; lower bound; orthogonal array; saturated array PDF BibTeX XML Cite \textit{F.-S. Chai} et al., Commun. Stat., Theory Methods 38, No. 20, 3725--3735 (2009; Zbl 1177.62091) Full Text: DOI References: [1] DOI: 10.2307/1266285 · Zbl 0109.12201 · doi:10.2307/1266285 [2] DOI: 10.1214/aoms/1177729331 · Zbl 0048.00803 · doi:10.1214/aoms/1177729331 [3] DOI: 10.1111/1467-9868.00303 · Zbl 1040.62064 · doi:10.1111/1467-9868.00303 [4] DOI: 10.1016/S0378-3758(99)00163-9 · Zbl 0964.62078 · doi:10.1016/S0378-3758(99)00163-9 [5] DOI: 10.1007/s001840300266 · Zbl 1042.62073 · doi:10.1007/s001840300266 [6] DOI: 10.1016/j.spl.2004.06.021 · Zbl 1116.62383 · doi:10.1016/j.spl.2004.06.021 [7] DOI: 10.1016/j.jspi.2006.11.002 · Zbl 1115.62077 · doi:10.1016/j.jspi.2006.11.002 [8] DOI: 10.1016/S0378-3758(02)00116-7 · Zbl 1127.62395 · doi:10.1016/S0378-3758(02)00116-7 [9] Mandal A., Statist. Sinica 15 pp 697– (2005) [10] DOI: 10.2307/1268904 · Zbl 0900.62416 · doi:10.2307/1268904 [11] DOI: 10.2307/3315731 · Zbl 0891.62054 · doi:10.2307/3315731 [12] DOI: 10.1214/009053605000000688 · Zbl 1084.62070 · doi:10.1214/009053605000000688 [13] DOI: 10.1214/aos/1013699993 · Zbl 1041.62067 · doi:10.1214/aos/1013699993 [14] DOI: 10.1016/S0167-7152(99)00038-3 · Zbl 0958.62071 · doi:10.1016/S0167-7152(99)00038-3 [15] DOI: 10.1016/S0378-3758(01)00248-8 · Zbl 0992.62069 · doi:10.1016/S0378-3758(01)00248-8 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.