Optimal designs for multivariate calibrations in multiresponse regression models
碩士 === 國立中山大學 === 應用數學系研究所 === 96 === 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 t...
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ndltd-TW-096NSYS55070222018-06-25T06:05:27Z http://ndltd.ncl.edu.tw/handle/k42a6m Optimal designs for multivariate calibrations in multiresponse regression models 在多重反應量的迴歸模型下對於多重校準的最適設計 Jia-Ming Guo 郭家銘 碩士 國立中山大學 應用數學系研究所 96 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. Chun-Sui Lin Mong-Na Lo Huang 林純穗 羅夢娜 2008 學位論文 ; thesis 29 en_US |
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碩士 === 國立中山大學 === 應用數學系研究所 === 96 === 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.
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Chun-Sui Lin |
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Chun-Sui Lin Jia-Ming Guo 郭家銘 |
author |
Jia-Ming Guo 郭家銘 |
spellingShingle |
Jia-Ming Guo 郭家銘 Optimal designs for multivariate calibrations in multiresponse regression models |
author_sort |
Jia-Ming Guo |
title |
Optimal designs for multivariate calibrations in multiresponse regression models |
title_short |
Optimal designs for multivariate calibrations in multiresponse regression models |
title_full |
Optimal designs for multivariate calibrations in multiresponse regression models |
title_fullStr |
Optimal designs for multivariate calibrations in multiresponse regression models |
title_full_unstemmed |
Optimal designs for multivariate calibrations in multiresponse regression models |
title_sort |
optimal designs for multivariate calibrations in multiresponse regression models |
publishDate |
2008 |
url |
http://ndltd.ncl.edu.tw/handle/k42a6m |
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