Title page for etd-0721108-190245


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URN etd-0721108-190245
Author Jia-Ming Guo
Author's Email Address m952040030@student.nsysu.edu.tw
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Department Applied Mathematics
Year 2007
Semester 2
Degree Master
Type of Document
Language English
Title Optimal designs for multivariate calibrations in
multiresponse regression models
Date of Defense 2008-06-19
Page Count 29
Keyword
  • prediction
  • scalar optimal design
  • c-criterion
  • multivariate calibration
  • locally optimal design
  • classical estimator
  • equivalence theorem
  • Abstract Consider a linear regression model with a two-dimensional control vector (x_1, x_2) and an m-dimensional response vector y = (y_1, . . . , y_m). The components of y are correlated with a known covariance matrix. Based on the assumed regression model, there are two problems of interest. The first one is to estimate unknown control vector x_c corresponding to an observed y, where xc will be estimated by the classical estimator. The second one is to obtain a suitable estimation of the control vector x_T corresponding to a given target T = (T_1, . . . , T_m) on the expected responses. Consideration in this work includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and defines the optimal control vector x, say x_T , to be the one which minimizes the weighted sum of squares of standardized deviations within the range of x. The objective of this study is to find c-optimal designs for estimating x_c and x_T , which minimize the mean squared error of the estimator of xc and x_T respectively. The comparison of the difference between the optimal calibration design and the optimal design for estimating x_T is provided. The efficiencies of the optimal calibration design relative to the uniform design are also presented, and so are the efficiencies of the optimal design for given target vector relative to the uniform design.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Fu-Chuen Chang - co-chair
  • Chun-Sui Lin - advisor
  • Mong-Na Lo Huang - advisor
  • Files
  • etd-0721108-190245.pdf
  • indicate accessible in a year
    Date of Submission 2008-07-21

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