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

Bronisław Ceranka; Małgorzata Graczyk

Biometrical Letters (2013)

  • Volume: 50, Issue: 2, page 127-136
  • ISSN: 1896-3811

Abstract

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In this paper, we study the relationships between regular A-optimal spring balance weighing designs and regular A-optimal chemical balance weighing designs. We give the basic relation between these designs in the case where the errors are uncorrelated and they have different variances. We give some examples of methods of construction of such designs.

How to cite

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Bronisław Ceranka, and Małgorzata Graczyk. "Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors." Biometrical Letters 50.2 (2013): 127-136. <http://eudml.org/doc/268755>.

@article{BronisławCeranka2013,
abstract = {In this paper, we study the relationships between regular A-optimal spring balance weighing designs and regular A-optimal chemical balance weighing designs. We give the basic relation between these designs in the case where the errors are uncorrelated and they have different variances. We give some examples of methods of construction of such designs.},
author = {Bronisław Ceranka, Małgorzata Graczyk},
journal = {Biometrical Letters},
keywords = {A-optimal design; chemical balance weighing design; spring balance weighing design; balanced incomplete block design; E-optimal design},
language = {eng},
number = {2},
pages = {127-136},
title = {Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors},
url = {http://eudml.org/doc/268755},
volume = {50},
year = {2013},
}

TY - JOUR
AU - Bronisław Ceranka
AU - Małgorzata Graczyk
TI - Relations between regular A-optimal chemical and spring balance weighing designs with diagonal covariance matrix of errors
JO - Biometrical Letters
PY - 2013
VL - 50
IS - 2
SP - 127
EP - 136
AB - In this paper, we study the relationships between regular A-optimal spring balance weighing designs and regular A-optimal chemical balance weighing designs. We give the basic relation between these designs in the case where the errors are uncorrelated and they have different variances. We give some examples of methods of construction of such designs.
LA - eng
KW - A-optimal design; chemical balance weighing design; spring balance weighing design; balanced incomplete block design; E-optimal design
UR - http://eudml.org/doc/268755
ER -

References

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  1. Abrego B., Fernandez-Merchant S., Neubauer G.N., Watkins W. (2003): D-optimal weighing designs for n = -1mod4 objects and a large number of weighings. Linear Algebra and its Applications 374: 175-218.[WoS] Zbl1025.62025
  2. Banerjee K.S. (1975): Weighing Designs for Chemistry, Medicine. Economics, Operations Research, Statistics. Marcel Dekker Inc., New York. Zbl0334.62030
  3. Ceranka B., Graczyk M. (2004): A-optimal chemical balance weighing design. Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensis, Mathematica 15: 41-54. 
  4. Ceranka B., Graczyk M., Katulska K. (2006): A-optimal chemical balance weighing design with nonhomogeneity of variances of errors. Statistics and Probability Letters 76: 653 - 665 Zbl1090.62074
  5. Ceranka B., Graczyk M., Katulska K. (2007): On certain A-optimal chemical balance weighing designs. Computational Statistics and Data Analysis 51: 5821-5827.[WoS] Zbl05560074
  6. Ceranka B., Katulska K. (2001): A-optimal chemical balance weighing design with diagonal covariance matrix of errors. Moda 6, Advances in Model Oriented Design and Analysis, A.C. Atkinson, P. Hackl, W.G. Mffller, eds., Physica-Verlag, Heidelberg, New York, 29-36. Chadjiconstantinidis S., Chadjipadelis T. (1994): A construction method of new D-A-optimal designs when N = 3mod4 and к < N-1. Discrete Mathematics 131: 39-50. 
  7. Graczyk M. (2011): A-optimal biased spring balance design. Kybernetika 47, 893-901. Zbl1274.62495
  8. Graczyk M. (2012a): Notes about A-optimal spring balance weighing design. Journal of Statistical Planning and Inference 142: 781-784. Zbl1232.62108
  9. Graczyk M. (2012b): Regular A-optimal spring balance weighing designs. Revstat 10: 323-333. Zbl1297.62173
  10. Jacroux M., Notz W. (1983): On the optimality of spring balance weighing designs. The Annals of Statistics 11: 970-978. Zbl0529.62064
  11. Kageyama S., Saha G.M. (1983): Note on the construction of optimum chemical balance weighing designs. Ann. Inst. Statist. Mat. 35A: 447-452. Zbl0553.62066
  12. Neubauer G.N., Pace R.G. (2010): D-optimal (0,1)-weighing designs for eight objects. Linear Algebra and its Applications 432: 2634-2657.[WoS] Zbl1185.62134
  13. Masaro J., Wong C.S. (2008): Robustness of A-optimal designs. Linear Algebra and its Applications 429: 1392-1408.[WoS] Zbl1145.62053
  14. Pukelsheim F. (1993): Optimal Design of Experiment. John Wiley and Sons, New York. Zbl0834.62068
  15. Raghavarao D. (1971): Constructions and Combinatorial Problems in Designs of Experiments. John Wiley Inc., New York. Zbl0222.62036
  16. Shah K.R., Sinha B.K. (1989): Theory of Optimal Designs. Springer-Verlag, Berlin. Zbl0688.62043

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