On certain A-optimal biased spring  balance weighing designs

Bronisław  Ceranka; Małgorzata  Graczyk

doi:https://doi.org/10.59170/stattrans-2014-022

On certain A-optimal biased spring balance weighing designs

Bronisław Ceranka Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland. , Małgorzata Graczyk Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland. Statistics in Transition new series, vol. 15, 2014, 2, pages: 317-326 Published online: 2 June 2014 https://doi.org/10.59170/stattrans-2014-022

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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.

KEYWORDS

A-optimal design, spring balance weighing design.

REFERENCES

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