Some constructions of nested balanced equireplicate block designs

Shivani Rai; Shakti Banerjee; Sanpei Kageyama

Discussiones Mathematicae Probability and Statistics (2003)

  • Volume: 23, Issue: 1, page 45-68
  • ISSN: 1509-9423

Abstract

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arious methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block structure. A comparison is shown in Table 1.

How to cite

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Shivani Rai, Shakti Banerjee, and Sanpei Kageyama. "Some constructions of nested balanced equireplicate block designs." Discussiones Mathematicae Probability and Statistics 23.1 (2003): 45-68. <http://eudml.org/doc/287755>.

@article{ShivaniRai2003,
abstract = {arious methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block structure. A comparison is shown in Table 1.},
author = {Shivani Rai, Shakti Banerjee, Sanpei Kageyama},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Balanced incomplete block (BIB) design; efficiency balanced (EB) design; variance balanced (VB) design; efficiency balanced ternary (EBT); variance balanced ternary (VBT); efficiency balanced quaternary (EBQ); variance balanced quaternary (VBQ); balanced incomplete block design; BIB; efficiency balanced; EB; variance balanced; VB; efficiency balanced ternary; EBT; variance balanced ternary; VBT; efficiency balanced quaternary; EBQ; variance balanced quaternary; VBQ},
language = {eng},
number = {1},
pages = {45-68},
title = {Some constructions of nested balanced equireplicate block designs},
url = {http://eudml.org/doc/287755},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Shivani Rai
AU - Shakti Banerjee
AU - Sanpei Kageyama
TI - Some constructions of nested balanced equireplicate block designs
JO - Discussiones Mathematicae Probability and Statistics
PY - 2003
VL - 23
IS - 1
SP - 45
EP - 68
AB - arious methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block structure. A comparison is shown in Table 1.
LA - eng
KW - Balanced incomplete block (BIB) design; efficiency balanced (EB) design; variance balanced (VB) design; efficiency balanced ternary (EBT); variance balanced ternary (VBT); efficiency balanced quaternary (EBQ); variance balanced quaternary (VBQ); balanced incomplete block design; BIB; efficiency balanced; EB; variance balanced; VB; efficiency balanced ternary; EBT; variance balanced ternary; VBT; efficiency balanced quaternary; EBQ; variance balanced quaternary; VBQ
UR - http://eudml.org/doc/287755
ER -

References

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  1. [1] L. Angelis, C. Moyssiadis and S. Kageyama, Constructions of generalized binary proper efficiency balanced block designs with two different replication numbers, Sankhy¯a Ser. B 56 (1994), 259-266. Zbl0835.62063
  2. [2] E.J.B. Billington and P.T. Robinson, A list of balanced ternary designs with R ≤ 15 and some necessary existence conditions, Ars Combinatoria 10 (1983), 235-258. Zbl0534.05010
  3. [3] T. Caliński and S. Kageyama, Block Designs: A Randomization Approach, Volume I: Analysis, Springer, New York 2003. Zbl1108.62318
  4. [4] T. Caliński and S. Kageyama, Block Designs: A Randomization Approach, Volume II: Design. Springer, New York 2003. Zbl1108.62318
  5. [5] C.J. Colbourn and M.J. Colbourn, Nested triple systems, Ars Combinatoria 16 (1983), 27-34. 
  6. [6] A. Dey, Theory of Block Designs, Wiley Eastern, New Delhi 1986. Zbl0653.05010
  7. [7] D.K. Ghosh K. Joshi and S. Kageyama, Ternary variance balanced designs through BIB and GD designs, J. Japan Statist. Soc. 23 (1993), 75-81. Zbl0786.62079
  8. [8] D.K. Ghosh and P.K. Karmakar, Some series of efficiency balanced designs, Austral. J. Statist. 30 (1988), 47-51. Zbl0649.62075
  9. [9] D.K. Ghosh A. Shah and S. Kageyama, Constructions of variance balanced designs and efficiency balanced block designs, J. Japan Statist. Soc. 24 (1994), 201-208. Zbl0818.62066
  10. [10] M. Jimbo and S. Kuriki, Constructions of nested designs, Ars Combinatoria 16 (1983), 275-285. Zbl0536.05010
  11. [11] S. Kageyama, On properties of efficiency-balanced designs, Commun. Statist. -Theor. Meth. A 9 (1980), 597-616. Zbl0433.62050
  12. [12] K. Katulska, Constructions of balanced ternary block designs, Discussiones Mathematicae - Algebra and Stochastic Methods 18 (1998), 167-177. Zbl0946.62071
  13. [13] J.Q. Longyear, A survey of nested designs, J. Statist. Plann. Inference 5 (1981), 181-187. Zbl0476.62062
  14. [14] J.P. Morgan, Nested designs, Handbook of Statistics, Design and Analysis of Experiments, Elsevier Science, Amsterdam, 13 (1996), 939-976. 
  15. [15] D.A. Preece, Nested balanced incomplete block designs, Biometrika 54 (1967), 479-486. 
  16. [16] D. Raghavarao, Constructions and Combinational Problems in Design of Experiments. Dover, New York 1988. 

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