TY - JOUR
T1 - Optimal selection and ordering of columns in supersaturated designs
AU - Niki, N.
AU - Iwata, M.
AU - Hashiguchi, H.
AU - Yamada, S.
N1 - Funding Information:
This study has been partly supported by Grant-in-Aid for Scientific Research (C) 21500271 , 2009, from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan . The authors would like to thank the editor and an anonymous reviewer who have read the manuscript carefully and provided useful comments for revision.
PY - 2011/7
Y1 - 2011/7
N2 - Two methods to select columns for assigning factors to work on supersaturated designs are proposed. The focus of interest is the degree of non-orthogonality between the selected columns. One method is the exhaustive enumeration of selections of p columns from all k columns to find the exact optimality, while the other is intended to find an approximate solution by applying techniques used in the corresponding analysis, aiming for ease of use as well as a reduction in the large computing time required for large k with the first method. Numerical illustrations for several typical design matrices reveal that the resulting "approximately" optimal assignments of factors to their columns are exactly optimal for any p. Ordering the columns in E(s2)-optimal designs results in promising new findings including a large number of E(s2)-optimal designs.
AB - Two methods to select columns for assigning factors to work on supersaturated designs are proposed. The focus of interest is the degree of non-orthogonality between the selected columns. One method is the exhaustive enumeration of selections of p columns from all k columns to find the exact optimality, while the other is intended to find an approximate solution by applying techniques used in the corresponding analysis, aiming for ease of use as well as a reduction in the large computing time required for large k with the first method. Numerical illustrations for several typical design matrices reveal that the resulting "approximately" optimal assignments of factors to their columns are exactly optimal for any p. Ordering the columns in E(s2)-optimal designs results in promising new findings including a large number of E(s2)-optimal designs.
KW - Corresponding analysis
KW - Exhaustive enumeration
KW - Factor assignment
KW - Non-orthogonality
KW - Optimal design
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U2 - 10.1016/j.jspi.2011.02.007
DO - 10.1016/j.jspi.2011.02.007
M3 - Article
AN - SCOPUS:79952251316
SN - 0378-3758
VL - 141
SP - 2449
EP - 2462
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 7
ER -