A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

Łukasz Smaga. "A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans." Biometrical Letters 53.2 (2016): 119-131. <http://eudml.org/doc/287153>.

@article{ŁukaszSmaga2016,
abstract = {This paper considers main effects plans used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. The assumptions are adopted that n ≡ 2 (mod 8) and k > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by Jacroux (2011a) to be D-optimal when (m − 2)(k − 2) + 2 ⩽ n ⩽ (m − 1)(k − 2) + 2. Here, we extend that result. For (m − 3)(k − 2) + 2 ⩽ n < (m − 2)(k − 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(m + 1) ⩽ n < (m − 3)(k − 2) + 2, indicating their good performance under the criterion of D-optimality.},
author = {Łukasz Smaga},
journal = {Biometrical Letters},
keywords = {blocked main effects plan; D-efficiency; D-optimality; Fischer’s inequality; Hadamard’s inequality; nonorthogonality},
language = {eng},
number = {2},
pages = {119-131},
title = {A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans},
url = {http://eudml.org/doc/287153},
volume = {53},
year = {2016},
}

TY - JOUR
AU - Łukasz Smaga
TI - A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans
JO - Biometrical Letters
PY - 2016
VL - 53
IS - 2
SP - 119
EP - 131
AB - This paper considers main effects plans used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. The assumptions are adopted that n ≡ 2 (mod 8) and k > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by Jacroux (2011a) to be D-optimal when (m − 2)(k − 2) + 2 ⩽ n ⩽ (m − 1)(k − 2) + 2. Here, we extend that result. For (m − 3)(k − 2) + 2 ⩽ n < (m − 2)(k − 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(m + 1) ⩽ n < (m − 3)(k − 2) + 2, indicating their good performance under the criterion of D-optimality.
LA - eng
KW - blocked main effects plan; D-efficiency; D-optimality; Fischer’s inequality; Hadamard’s inequality; nonorthogonality
UR - http://eudml.org/doc/287153
ER -