Yeh and Bradley conjectured that every binary connected block design with blocks of size $k$ and a constant replication number $r$ for each treatment can be converted to a linear trend-free design by permuting the positions of treatments within blocks if and only if $r(k + 1) \equiv 0 (\operatorname{mod} 2)$. This conjecture is studied. Results include: (i) the conjecture is true whenever the block size is even and (ii) the conjecture is true for BIB designs.
Publié le : 1993-12-14
Classification:
Elimination of trend effect,
system of distinct representatives,
universal optimality,
BIB design,
BBD,
62K10,
62K05,
05B05
@article{1176349411,
author = {Chai, Feng-Shun and Majumdar, Dibyen},
title = {On the Yeh-Bradley Conjecture on Linear Trend-Free Block Designs},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 2087-2097},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349411}
}
Chai, Feng-Shun; Majumdar, Dibyen. On the Yeh-Bradley Conjecture on Linear Trend-Free Block Designs. Ann. Statist., Tome 21 (1993) no. 1, pp. 2087-2097. http://gdmltest.u-ga.fr/item/1176349411/