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A-optimal chemical balance weighing design with nonhomogeneity of variances of errors

Author

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  • Ceranka, Bronislaw
  • Graczyk, Malgorzata
  • Katulska, Krystyna

Abstract

The problem studied in the paper concerns the estimation of individual weights of p objects according to the model of an A-optimal chemical balance weighing design with a positive definite diagonal variance matrix of errors under the restriction p1+p2=q[less-than-or-equals, slant]p, where p1 and p2 represent the numbers of objects placed on the left and on the right pan, respectively, in each of the measurement operations. The lower bound of tr(X'G-1X)-1 is obtained and the necessary and sufficient condition for this lower bound to be attained is given. To construct the A-optimal chemical balance weighing design the incidence matrices of the balanced bipartite weighing designs are used.

Suggested Citation

  • Ceranka, Bronislaw & Graczyk, Malgorzata & Katulska, Krystyna, 2006. "A-optimal chemical balance weighing design with nonhomogeneity of variances of errors," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 653-665, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:7:p:653-665
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    Cited by:

    1. Łukasz Smaga, 2016. "A note on D-optimal chemical balance weighing designs with autocorrelated observations," Statistical Papers, Springer, vol. 57(3), pages 721-730, September.

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