URN 
etd0721108190245 
Author 
JiaMing 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 
20080619 
Page Count 
29 
Keyword 
prediction
scalar optimal design
ccriterion
multivariate calibration
locally optimal design
classical estimator
equivalence theorem

Abstract 
Consider a linear regression model with a twodimensional control vector (x_1, x_2) and an mdimensional 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 coptimal 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 
MeiHui Guo  chair
FuChuen Chang  cochair
ChunSui Lin  advisor
MongNa Lo Huang  advisor

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indicate accessible in a year 
Date of Submission 
20080721 