TY - JOUR

T1 - Exact D-optimal designs for weighted polynomial regression model

AU - Chen, Ray-Bing

AU - Huang, Mong Na Lo

N1 - Funding Information:
Research supported in part by the National Science Council of the Republic of China, Grant No. NSC 85-2121-M110-017

PY - 2000/4/28

Y1 - 2000/4/28

N2 - In this work, the exact D-optimal designs for weighted polynomial regression are investigated. In Gaffke (1987, J. Statist. Planning Inference 15, 189-204) a sufficient condition has been given that Salaeveskiǐ's type of result about the exact D-optimal designs holds when sample size n is large enough. Here we provide another sufficient condition for checking if Salaeveskiǐ's type of result still holds for weighted polynomial models, where it is a stronger condition and may not be as general as in Gaffke (1987, J. Statist. Planning Inference 15, 189-204) but can be used easily to give an efficient method to determine the sample size guaranteeing the result to be valid. A table of minimum sample sizes needed by our method is given for some weight functions, which are also shown numerically to be the same as the minimum sample sizes needed by Gaffke's condition in those cases. Finally for the no-intercept model as considered in Huang et al. (1995, Statistica Sinica, 441-458) the exact D-optimal designs on intervals [a,1],0≤a<1, and [-1,1] are also discussed.

AB - In this work, the exact D-optimal designs for weighted polynomial regression are investigated. In Gaffke (1987, J. Statist. Planning Inference 15, 189-204) a sufficient condition has been given that Salaeveskiǐ's type of result about the exact D-optimal designs holds when sample size n is large enough. Here we provide another sufficient condition for checking if Salaeveskiǐ's type of result still holds for weighted polynomial models, where it is a stronger condition and may not be as general as in Gaffke (1987, J. Statist. Planning Inference 15, 189-204) but can be used easily to give an efficient method to determine the sample size guaranteeing the result to be valid. A table of minimum sample sizes needed by our method is given for some weight functions, which are also shown numerically to be the same as the minimum sample sizes needed by Gaffke's condition in those cases. Finally for the no-intercept model as considered in Huang et al. (1995, Statistica Sinica, 441-458) the exact D-optimal designs on intervals [a,1],0≤a<1, and [-1,1] are also discussed.

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U2 - 10.1016/S0167-9473(99)00054-7

DO - 10.1016/S0167-9473(99)00054-7

M3 - Article

AN - SCOPUS:0033734780

SN - 0167-9473

VL - 33

SP - 137

EP - 149

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

IS - 2

ER -