Title page for etd-0718108-034851


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URN etd-0718108-034851
Author You-Yi Chang
Author's Email Address jerrysix321@yahoo.com.tw
Statistics This thesis had been viewed 5110 times. Download 842 times.
Department Applied Mathematics
Year 2007
Semester 2
Degree Master
Type of Document
Language English
Title D- and A-Optimal Designs for Models in Mixture Experiments with Correlated Observations
Date of Defense 2008-06-19
Page Count 41
Keyword
  • polynomial models for mixture experiments
  • log contrast model
  • D-optimality
  • Scheff'e model
  • A-optimality
  • Abstract 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 Σx_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.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Fu-Chuen Chang - co-chair
  • Chun-Sui Lin - co-chair
  • Mong-Na Lo Huang - advisor
  • Files
  • etd-0718108-034851.pdf
  • indicate accessible in a year
    Date of Submission 2008-07-18

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