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D- and A-Optimal Designs for Models in Mixture Experiments with Correlated Observations

A mixture experiment is an experiment in which the q-ingredients {x_i,i=1,2,...,q} are nonnegative and ubject to the simplex restriction £Ux_i=1 on the (q-1)-dimensional probability simplex S^{q-1}. It is usually assumed that the observations are uncorrelated, although in many applications the observations are correlated. We study the difference between the
ordinary least square estimator and the Gauss Markov estimator under correlated observations. It is shown that for certain models and a special covariance structure for the mixture experiments, the
unknown parameter vector for the ordinary least square estimators and the Gauss Markov estimators are the same. Moreover, we also show that the corresponding optimal designs may be obtained from previous D- and A-optimal designs for uncorrelated observations. The models studied here includ Scheff'e models, log contrast models, models containing homogeneous functions, and models containing inverse terms.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0718108-034851
Date18 July 2008
CreatorsChang, You-Yi
ContributorsChun-Sui Lin, Mei-Hui Guo, Mong-Na Lo Huang, Fu-Chuen Chang
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0718108-034851
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