| Title:
|
A-optimal biased spring balance weighing design (English) |
| Author:
|
Graczyk, Małgorzata |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
6 |
| Year:
|
2011 |
| Pages:
|
893-901 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the problem of estimation of individual measurements of objects in a biased spring balance weighing design under assumption that the errors are uncorrelated and they have different variances. The lower bound for the variance of each of the estimated measurements for this design and the necessary and sufficient conditions for this lower bound to be attained are given. The incidence matrices of the balanced incomplete block designs are used for construction of the A-optimal biased spring balance weighing design. (English) |
| Keyword:
|
A-optimal design |
| Keyword:
|
biased design |
| Keyword:
|
spring balance weighing design |
| MSC:
|
62K05 |
| MSC:
|
62K10 |
| idZBL:
|
Zbl 06047593 |
| idMR:
|
MR2907849 |
| . |
| Date available:
|
2011-12-08T10:02:06Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141732 |
| . |
| Reference:
|
[1] Banerjee, K. S.: Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics.Marcel Dekker Inc., New York 1975. Zbl 0334.62030, MR 0458751 |
| Reference:
|
[2] Ceranka, B., Katulska, K.: Optimum spring balance weighing designs with non-homogeneity of the variances of errors.J. Statist. Plann. Inference 30 (1992), 185–193. MR 1157759, 10.1016/0378-3758(92)90080-C |
| Reference:
|
[3] Ceranka, B., Katulska, K.: A-optimal chemical balance weighing designs with diagonal covariance matrix of errors.In: MODA 6 (A. C. Atkinson, P. Hackl, W. G. Muller, eds.), Physica, Heidelberg 2001, pp. 29–36. MR 1865143 |
| Reference:
|
[4] Ceranka, B., Graczyk, M., Katulska, K.: A-optimal chemical balance weighing design with nonhomogeneity of variances of errors.Statist. Probab. Lett. 76 (2006), 653–665. Zbl 1090.62074, MR 2234783, 10.1016/j.spl.2005.09.012 |
| Reference:
|
[5] Pukelsheim, F.: Optimal Design of Experiment.John Wiley and Sons, New York 1993. MR 1211416 |
| Reference:
|
[6] Raghavarao, D.: Constructions and Combinatorial Problems in Designs of Experiments.John Wiley Inc., New York 1971. MR 0365935 |
| Reference:
|
[7] Shah, K. R., Sinha, B. K. : Theory of Optimal Designs.Springer-Verlag, Berlin 1989. Zbl 0688.62043, MR 1016151 |
| . |
