D-Optimal designs for a multivariate regression model

Krafft, Olaf; Schaefer, Martin

doi:10.1016/0047-259x(92)90083-r

Cited by 43 publications

(19 citation statements)

References 3 publications

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“…The prior information used for finding the optimal designs is very helpful for increasing the efficiency of the design while comparing to a uniform design. Krafft and Schaefer [24] has shown that under rather mild assumptions the D-optimal designs for a multiresponseunivariate linear regression model do not depend on the covariance matrix of response variables. In this work, it is observed that the level of the correlation of the dual response does make some differences on the corresponding optimal design.…”

Section: Discussionmentioning

confidence: 99%

Optimal designs for estimating the control values in multi-univariate regression models

Lin

Huang

2010

Journal of Multivariate Analysis

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a b s t r a c tThis paper considers a linear regression model with a one-dimensional control variablex 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, it is of interest to obtain a suitable estimation of the corresponding control value for a given target vector T = (T 1 , . . . , T m ) on the expected responses. Due to the fact that there is more than one target value to be achieved in the multiresponse case, the m expected responses may meet their target values at different respective control values. Consideration on the performance of an estimator for the control value includes the difference of the expected response E(y i ) from its corresponding target value T i for each component and the optimal value of control point, say x 0 , is defined to be the one which minimizes the weighted sum of squares of those standardized differences within the range of x. The objective of this study is to find a locally optimal design for estimating x 0 , which minimizes the mean squared error of the estimator of x 0 . It is shown that the optimality criterion is equivalent to a ccriterion under certain conditions and explicit solutions with dual response under linear and quadratic polynomial regressions are obtained.

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Section: Discussionmentioning

confidence: 99%

Optimal designs for estimating the control values in multi-univariate regression models

Lin

Huang

2010

Journal of Multivariate Analysis

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“…Another important auxiliary result is a determinantal formula for covariance matrices. This formula was first established in [12] and a different proof and several related results were subsequently found by Bischoff [1].…”

Section: Introductionmentioning

confidence: 90%

“…But if n=8p\1 or n=8p+4, then the D-optimum designs fail to be symmetric and a more intricate analysis which accommodates this fact is required. If n=8p+2, the D-optimum designs are again symmetric, but the inequalities used in [12] appear to be not quite sufficient in this case either. The D-optimum n-point designs for all the values of n not covered in [12] are given in Theorems 1 and 2 in the next section.…”

Section: Introductionmentioning

confidence: 91%

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Optimum Designs for a Multiresponse Regression Model

Imhof

2000

Journal of Multivariate Analysis

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Exact n-point designs are given which are D-optimum for a simple multiresponse model, where the individual response variables can be represented by first-order and second-order models. The present results complement recent findings by Krafft and Schaefer, who obtained D-optimum n-point designs for several values of n. Furthermore, a conjecture on G-optimum n-point designs is given and the conjecture is proved for the simplest non-trivial case, that is, for n=4. Academic PressAMS 1991 subject classifications: 62K05, 62H99.

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“…That the conjecture does hold for cubic regression was shown by CONSTANTINE, LIM and STUDDEN (1987). KRAFFT and SCHAEFER (1992) and IMHOF (2000a) examined a linear-quadratic multivariate model and found several exact D-optimal designs. It turned out that for this model no Salaevskii type result can be established.…”

Section: Introductionmentioning

confidence: 97%

Efficiencies of Rounded Optimal Approximate Designs for Small Samples

Imhof

López–Fidalgo

Wong

2001

Statistica Neerlandica

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Optimal exact designs are notoriously hard to study and only a few of them are known for polynomial models. Using recently obtained optimal exact designs (IMHOF, 1997), we show that the ef®ciency of the frequently used rounded optimal approximate designs can be sensitive if the sample size is small. For some criteria, the ef®ciency of the rounded optimal approximate design can vary by as much as 25% when the sample size is changed by one unit. The paper also discusses lower ef®ciency bounds and shows that they are sometimes the best possible bounds for the rounded optimal approximate designs.

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D-Optimal designs for a multivariate regression model

Cited by 43 publications

References 3 publications

Optimal designs for estimating the control values in multi-univariate regression models

Optimal designs for estimating the control values in multi-univariate regression models

Optimum Designs for a Multiresponse Regression Model

Efficiencies of Rounded Optimal Approximate Designs for Small Samples

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