The estimation problem of individual weights of objects in spring balance weighing design using the criterion of D-optimality is discussed. It is assumed that variances of errors are not equal and errors are not correlated. The upper bound of the determinant of the information matrix of estimators is obtained and the conditions for this upper bound to be attained are proved. Some methods of constructions regular D-optimal spring balance weighing designs are demonstrated.
AMS Subject Classification
Primary: 62K05 Secondary: 05B05
D-optimal design Spring balance weighing design
This is a preview of subscription content, log in to check access.
Banerjee, K. S., 1975. Weighing Design for Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker Inc., New York.zbMATHGoogle Scholar
Harville D. A., 1997. Matrix Algebra from a Statistician’s Perspective. Springer-Verlag, New York, Inc.CrossRefGoogle Scholar
Hudelson, M., Klee V., Larman D., 1996. Largest j-simplices in d-cubes: Some relatives of the Hadamard determinant problem. Linear Algebra and its Applications, 241, 519–598.MathSciNetCrossRefGoogle Scholar
Jacroux, M., Notz, W., 1983. On the optimality of spring balance weighing designs. The Annals of Statistics, Vol. 11, No. 3, 970–978.MathSciNetCrossRefGoogle Scholar
Neubauer, M. G., Watkins, W., Zeitlin, J., 1997. Maximal j-simplices in the real d-dimensional unit cube. Journal of Combinatorial Theory, Ser. A 80, 1–12.MathSciNetCrossRefGoogle Scholar