Optimal design is studied for factorial experiments in the nested row and column setting. The approach is analogous to that of orthogonal Latin squares: main effects plans are found by the superimposition of one nested row and column design upon another. Conditions are stated for statistical orthogonality of the superimposed components, resulting in orthogonal main effects plans, and a number of constructions are given. Orthogonal collections of sets of Latin squares are introduced. All of the constructed designs are also optimal main effects plans for the row-column and the unstructured block design settings. Further applications are as optimal multidimensional
incomplete block designs and as optimal designs for multistage experimentation.
Publié le : 1996-06-14
Classification:
Balanced incomplete block design,
bottom-stratum universally optimal nested row and column design,
Latin square,
optimal design,
orthogonality,
Youden design,
62K05,
62K15,
62K10,
62K99
@article{1032526963,
author = {Morgan, J. P. and Uddin, Nizam},
title = {Optimal blocked main effects plans with nested rows and columns and related designs},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 1185-1208},
language = {en},
url = {http://dml.mathdoc.fr/item/1032526963}
}
Morgan, J. P.; Uddin, Nizam. Optimal blocked main effects plans with nested rows and columns and related designs. Ann. Statist., Tome 24 (1996) no. 6, pp. 1185-1208. http://gdmltest.u-ga.fr/item/1032526963/