TY - JOUR
T1 - Optimal multi-criteria designs for Fourier regression models
AU - Shi, Peide
AU - Fang, Kai-Tai
AU - Tsai, Chih-Ling
N1 - Funding Information:
We are grateful to the referees and the Associate Editor for their constructive comments and suggestions. The research of Peide Shi was partially supported by a postdoctoral fellowship from the Statistics Research and Consultancy Centre of Hong Kong Baptist University, and the National Science Foundation grant of China. The research of Kai-Tai Fang was supported by a Hong Kong UGC-RGC grant.
PY - 2001/7/1
Y1 - 2001/7/1
N2 - Riccomagno, Schwabe and Wynn (RSW) (1997) have given a necessary and sufficient condition for obtaining a complete Fourier regression model with a design based on lattice points that is D-optimal. However, in practice, the number of factors to be considered may be large, or the experimental data may be restricted or not homogeneous. To address these difficulties we extend the results of RSW to obtain a sufficient condition for an incomplete interaction Fourier model design based on lattice points that is D-, A-, E- and G-optimal. We also propose an algorithm for finding such optimal designs that requires fewer design points than those obtained using RSW's generators when the underlying model is a complete interaction model.
AB - Riccomagno, Schwabe and Wynn (RSW) (1997) have given a necessary and sufficient condition for obtaining a complete Fourier regression model with a design based on lattice points that is D-optimal. However, in practice, the number of factors to be considered may be large, or the experimental data may be restricted or not homogeneous. To address these difficulties we extend the results of RSW to obtain a sufficient condition for an incomplete interaction Fourier model design based on lattice points that is D-, A-, E- and G-optimal. We also propose an algorithm for finding such optimal designs that requires fewer design points than those obtained using RSW's generators when the underlying model is a complete interaction model.
KW - Fourier regression model
KW - Lattice point
KW - Optimal design
UR - http://www.scopus.com/inward/record.url?scp=0035402388&partnerID=8YFLogxK
U2 - 10.1016/S0378-3758(00)00212-3
DO - 10.1016/S0378-3758(00)00212-3
M3 - Journal article
AN - SCOPUS:0035402388
SN - 0378-3758
VL - 96
SP - 387
EP - 401
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 2
ER -