A-optimal Chemical Balance Weighing Designs with Diagonal Covariance Matrix of Errors

Ceranka, Bronisław; Katulska, K.

doi:10.1007/978-3-642-57576-1_4

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…The above result was originally proved by Ceranka and Katulska in 2001. For the case of a biased spring balance weighing design X we have the following result.…”

Section: Introductionmentioning

confidence: 79%

“…The concept of the A-optimality has been discussed in the literature. The best general references are Jacroux and Notz (1983), Ceranka and Katulska (2001), Ceranka and Graczyk (2004), Ceranka et al (2006Ceranka et al ( , 2007, Masaro and Wong (2008), and Graczyk (2011Graczyk ( , 2012a.…”

Section: Introductionmentioning

confidence: 99%

“…In the remainder of the paper we shall consider G to be an n n  positive definite diagonal matrix. Ceranka and Katulska (2001) showed that for any nonsingular chemical balance weighing design X with the covariance matrix…”

Section: Introductionmentioning

confidence: 99%

“…The basic ideas and elementary properties of weighing designs are presented, for instance, in Jacroux and Notz (1983), Kageyama and Saha (1983), Ceranka and Katulska (2001) and Graczyk (2011…”

Section: Introductionmentioning

confidence: 99%

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Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

Ceranka

Graczyk

2013

Biometrical Letters

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“…The above result was originally proved by Ceranka and Katulska in 2001. For the case of a biased spring balance weighing design X we have the following result.…”

Section: Introductionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

Ceranka

Graczyk

2013

Biometrical Letters

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“…Because of the properties of weighing designs, the matrix of experimental . From Ceranka and Katulska (2001), d X is the matrix of a regular A-optimal design.…”

Section: Application Of Chemical Balance Weighing Designsmentioning

confidence: 99%

Some applications of weighing designs

Graczyk

2013

Biometrical Letters

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The purpose of this paper is to apply results on weighing designs to the setting of 2 m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.Key words: chemical balance weighing design, factorial design, spring balance weighing design. We now apply Theorem 3.4 (ii) for 3 0 x  . We obtain

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Regular A-optimal design matrices X = (x ij ) with x ij = −1, 0, 1

Graczyk

2009

Stat Papers

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A-optimal Chemical Balance Weighing Designs with Diagonal Covariance Matrix of Errors

Cited by 4 publications

References 2 publications

Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors

Some applications of weighing designs

Regular A-optimal design matrices X = (x ij ) with x ij = −1, 0, 1

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