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Exact D-optimal designs for weighted polynomial regression model

✍ Scribed by Ray-Bing Chen; Mong-Na Lo Huang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
137 KB
Volume
33
Category
Article
ISSN
0167-9473

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✦ Synopsis

In this work, the exact D-optimal designs for weighted polynomial regression are investigated. In Ga ke (1987, J. Statist. Planning Inference 15, 189 -204) a su cient condition has been given that Salaeveski Γ„ i's type of result about the exact D-optimal designs holds when sample size n is large enough. Here we provide another su cient condition for checking if Salaeveski Γ„ i's type of result still holds for weighted polynomial models, where it is a stronger condition and may not be as general as in Ga ke (1987, J. Statist. Planning Inference 15, 189 -204) but can be used easily to give an e cient 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 Ga ke'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 Β‘ 1; and [ -1; 1] are also discussed.

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