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A-optimal chemical balance weighing design with correlated errors

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Abstract

In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound oftr (X′G −1 X)−1 is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.

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References

  1. K. S. Banerjee,Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker Inc., New York, 1975.

    MATH  Google Scholar 

  2. B. Ceranka and K. Katulska,A-optimal chemical balance weighing designs with diagonal covariance matrix of errors, MODA 6, A. C. Atkinson, P. Hackl and W. G. Mller, eds., Physical, Heidelberg, 2001.

    Google Scholar 

  3. C. S. Cheng,Optimality of certain assymetrical experimental designs. Ann. Statist.6 (1978), 1239–1261.

    Article  MATH  MathSciNet  Google Scholar 

  4. Z. Gail and J. Kiefer,D-optimum weighing designs Ann. Statist.8 (1980), 1293–1306.

    Article  MathSciNet  Google Scholar 

  5. H. Hotelling,Some improvements in weighing designs and other experimental techniques, Ann. Math. Stat.15 (1944), 297–305.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Kiefer,General equivalence theory for optimum design (approximate theory). Ann. Statist.2 (1974), 849–874.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Raghavarao,Constructions and Combinatorial Problems in Designs of Experiments. John Wiley Inc., New York, 1971.

    Google Scholar 

  8. S. C. Wong and J. C. Masaro,A—optimal matrices X=(x ij )Nxn with x ij =−1,0,1, Linear and Multilinear Algebra15 (1984), 23–46.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical and Statistical Methods, Agricultural University of Poznań, ul. Wojska Polskiego 28, 60-637, Poznań, Poland

    Bronislaw Ceranka & Malgorzata Graczyk

Authors
  1. Bronislaw Ceranka
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  2. Malgorzata Graczyk
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Corresponding author

Correspondence to Bronislaw Ceranka.

Additional information

Bronislaw Ceranka, received his doctor title in 1972 from the Adam Mickiewicz University in Poznań, his professor title in 1991 from the Agricultural University of Poznań, Poland. His research interests are the experimental designs and applications of them. Also he does statistical consulting professor.

Malgorzata Graczyk, received her doctor title in 2002 from the Adam Mickiewicz University in Poznań, Poland.

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Ceranka, B., Graczyk, M. A-optimal chemical balance weighing design with correlated errors. JAMC 16, 143–150 (2004). https://doi.org/10.1007/BF02936157

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  • DOI: https://doi.org/10.1007/BF02936157

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