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2004 | 24 | 2 | 215-232
Tytuł artykułu

Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study the estimation problem of individual measurements (weights) of objects in a model of chemical balance weighing design with diagonal variance - covariance matrix of errors under the restriction k₁ + k₂ < p, where k₁ and k₂ represent the number of objects placed on the right and left pans, respectively. We want all variances of estimated measurments to be equal and attaining their lower bound. We give a necessary and sufficient condition under which this lower bound is attained by the variance of each of the estimated measurements. To construct the design matrix X of the considered optimum chemical balance weighing design we use the incidence matrices of balanced bipartite weighing designs.
Kategorie tematyczne
Rocznik
Tom
24
Numer
2
Strony
215-232
Opis fizyczny
Daty
wydano
2004
otrzymano
2004-01-10
poprawiono
2004-08-04
Twórcy
  • Department of Mathematical and Statistical Methods, Agricultural University, Wojska Polskiego 28, 60-637 Poznań, Poland
  • Department of Mathematical and Statistical Methods, Agricultural University, Wojska Polskiego 28, 60-637 Poznań, Poland
Bibliografia
  • [1] K.S. Banerjee, Weighing Designs for Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker Inc., New York 1975.
  • [2] B. Ceranka and M. Graczyk, Optimum chemical balance weighing designs under the restriction on weighings, Discussiones Mathematicae - Probability and Statistics 21 (2001), 111-120.
  • [3] B. Ceranka and K. Katulska, Chemical balance weighing designs under the restriction on the number of objects placed on the pans, Tatra Mt. Math. Publ. 17 (1999), 141-148.
  • [4] B. Ceranka, K. Katulska and D. Mizera, The application of ternary balanced block designs to chemical balance weighing designs, Discussiones Mathematicae - Algebra and Stochastic Methods 18 (1998), 179-185.
  • [5] H. Hotelling, Some improvements in weighing and other experimental techniques, Ann. Math. Stat. 15 (1944), 297-305.
  • [6] C. Huang, Balanced bipartite weighing designs, Journal of Combinatorial Theory (A) 21 (1976), 20-34.
  • [7] K. Katulska, Optimum chemical balance weighing designs with non - homegeneity of the variances of errors, J. Japan Statist. Soc. 19 (1989), 95-101.
  • [8] J.W. Linnik, Metoda Najmniejszych Kwadratów i Teoria Opracowywania Obserwacji, PWN, Warszawa 1962.
  • [9] D. Raghavarao, Constructions and Combinatorial Problems in Design ofExperiments, John Wiley Inc., New York 1971.
  • [10] C.R. Rao, Linear Statistical Inference and its Applications, Second Edition, John Wiley and Sons, Inc., New York 1973.
  • [11] M.N. Swamy, Use of balanced bipartite weighing designs as chemical balance designs, Comm. Statist. Theory Methods 11 (1982), 769-785.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1054
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