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On Certain A-Optimal Biased Spring Balance Weighing Designs

Author

Listed:
  • Bronisław Ceranka
  • Małgorzata Graczyk

Abstract

In the paper, the estimation of unknown measurements of p objects in the experiment, according to the model of the spring balance weighing design, is discussed. The weighing design is called biased if the first column of the design matrix has elements equal to one only. The A-optimal design is a design in which the trace of the inverse of information matrix is minimal. The main result is the broadening of the class of experimental designs so that we are able to determine the regular A-optimal design. We give the lowest bound of the covariance matrix of errors and the conditions under which this lowest bound is attained. Moreover, we give new construction methods of theregular A-optimal spring balance weighing design based on the incidence matrices of the balanced incomplete block designs. The example is also given.

Suggested Citation

  • Bronisław Ceranka & Małgorzata Graczyk, 2014. "On Certain A-Optimal Biased Spring Balance Weighing Designs," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(2), pages 317-326, March.
    • Handle: RePEc:csb:stintr:v:15:y:2014:i:2:p:317-326
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    References listed on IDEAS

    as
    1. Ceranka, Bronislaw & Katulska, Krystyna, 1990. "Constructions of optimum biased spring balance weighing designs with the diagonal covariance matrix of errors," Computational Statistics & Data Analysis, Elsevier, vol. 10(2), pages 121-131, October.
    2. Katulska, Krystyna, 1989. "Optimum biased spring balance weighing designs," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 267-271, August.
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