Optimality of Some Row–Column Designs
Tóm tắt
Latin squares, Youden squares, and Generalized Youden designs are optimal row–column designs sharing a common characteristic: in each case the two component block designs determined by rows and columns are restricted to the special types of balanced block design known as BIBDs, RCBDs, or more generally BBDs. This article takes up the optimality problem when it is possible to have a BIBD column component, but only a less balanced competitor, known as GGDD, as row component design. A-optimality is established in most cases considered, and E-optimality in all.
Tài liệu tham khảo
Agrawal H (1966) Some generalizations of distinct representatives with applications to statistical designs. Ann Math Stat 37:525–528
Bagchi B, Bagchi S (2001) Optimality of partial geometric designs. Ann Stat 29(2):577–594
Chai F-S (1998) A note on generalization of distinct representatives. Stat Probab Lett 39(2):173–177
Chai F-S, Cheng C-S (2011) Some optimal row-column designs. J Stat Theory Pract 5(1):59–67
Cheng CS (1978) Optimality of certain asymmetrical experimental designs. Ann Statist 6(6):1239–1261
Dean A, Voss D, Draguljić D (2017) Design Anal Experiment, 2nd edn. Springer Texts in Statistics. Springer, Cham
Jacroux M (1982) Some E-optimal designs for the one-way and two-way elimination of heterogeneity. J Royal Stat Soc, Series B 44(2):253–261
Jacroux M (1985) Some sufficient conditions for the type \(1\) optimality of block designs. J Stat Plann Inference 11(3):385–398
Kiefer J (1975) Construction and optimality of generalized Youden designs. A Survey Stat Design Linear Models. North-Holland, Amsterdam, pp 333–353
Marshall AW, Olkin I, Arnold BC (2011) Inequalities: Theory of Majorization and its Applications, 2nd edn. Springer Series in Statistics, Springer, New York
Morgan JP (2015) Blocking with independent responses. Handbook of Design and Analysis of Experiments. CRC Press, Boca Raton, pp 99–157
Morgan JP, Jermjitpornchai S (2021) Optimal row-column designs with three rows. Stat Appl 19(1):257–275
Morgan JP, Reck B (2007) E-optimal design in irregular BIBD settings. J Stat Plan Inference 137(5):1658–1668
Morgan JP, Srivastav SK (2000) On the type-1 optimality of nearly balanced incomplete block designs with small concurrence range. Stat Sinica 10(4):1091–1116
Morgan JP, Stallings JW (2014) On the \(A\) criterion of experimental design. J Stat Theory Pract 8(3):418–422
Oehlert GW (2000) A First Course in Design and Analysis of Experiments. W. H, Freeman, New York
Russell KG (1980) Further results on the connectedness and optimality of designs of type \(O:XB\). Comm Stat A-Theory Methods 9(4):439–447
Shah KR, Sinha BK (1989) Theory of Optimal Designs. Lecture Notes in Statisitics, vol 54. Springer-Verlag, New York
Tomić M (1949) Théorème de Gauss relatif au centre de gravité et son application. Bull Soc Math Phys Serbie 1:31–40