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

Graczyk, Małgorzata

doi:10.1007/s00362-009-0248-2

Cited by 4 publications

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“…Many problems related to the properties of chemical balance weighing designs, spring balance weighing designs and some aspects of estimation of parameters can be found in the literature; see Kiefer (1974), Banerjee (1975), Katulska (1989), Sathe and Shenoy (1990), Koukouvinos (1995), Graczyk (2001, 2003), Graczyk (2009Graczyk ( , 2011Graczyk ( , 2012a. Some applications of weighing designs have been reported, for instance, in Beckman (1973), Banerjee (1975), Sloane and Harwit (1976), Katulska (1984), Katulska (1987a, b, 1989), Koukouvinos (1997).…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Some applications of weighing designs

Graczyk

2013

Biometrical Letters

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“…An example of experiment (chemical process) described by the aforementioned model can be found in Jenkins and Chanmugam (1962). There are also papers in the literature relating to designs with other forms of Cov(e) (see, for example, Ceranka et al 2006;Graczyk 2009;Masaro and Wong 2008) and spring balance weighing designs with (0, 1)-design matrices (see, for instance, Graczyk 2012; Lopez and Neubauer 2010). The applications of weighing designs (in chemistry, medicine, economics, operations research etc.)…”

Section: Introductionmentioning

confidence: 99%

A note on D-optimal chemical balance weighing designs with autocorrelated observations

Smaga

2015

Stat Papers

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In this paper, D-optimal chemical balance weighing designs with three objects are considered. The error terms are assumed to form a first-order autoregressive process, which implies that the covariance matrix of the vector of errors depends on the known parameter ρ. It is shown that the designs constructed by Katulska and Smaga (Metrika 76:393-407, 2013) are still D-optimal weighing designs with three objects under a wider interval of possible values for parameter ρ than that considered in that paper. Those designs are also proved to be highly D-efficient designs, when D-optimal design is not known.

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Uniquely E-optimal designs with n≡2(mod4) correlated observations

Smaga

2015

Linear Algebra and its Applications

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

Cited by 4 publications

References 4 publications

Some applications of weighing designs

Some applications of weighing designs

A note on D-optimal chemical balance weighing designs with autocorrelated observations

Uniquely E-optimal designs with n≡2(mod4) correlated observations

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