Abstract
TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established.
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i)
A group divisible design with λ2 = λ1 + 1.
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ii)
A group divisible design with λ1 = λ2 + 1 and group size 2.
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iii)
A linked block design.
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iv)
The dual of design (i)
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v)
The dual of design (ii).
All these designs are known to satisfy the same optimality property under fixed effects model whenk<v, while the design (i) is known to beE-optimal even whenk>v. From the results proved here, theE-optimality of designs (ii, (iii), (iv) and (v) under fixed effects model in the situation whenk >v also follows.
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References
Bose RC (1975) In: Combined intra and inter block estimation of treatment effects in incomplete block designs. A survey of statistical designs and linear models. J N Srivastava, Edited, pp 31
Cheng CS (1978) Optimality of certain asymmetrical designs. Ann Statist 6:1239
Cheng CS (1980) On theE-optimality of some block designs. Jour Roy Stat Soc 13/42:199
Constantine GM (1981) SomeE-optimal block designs. Ann Statist 9:886
Jacroux M (1980) On theE-optimality of regular graph designs. Jour Roy Stat Soc B 42:205
John JA, Mitchell TJ (1977) Optimal incomplete block designs. Jour Roy Soc B:29
Kiefer J (1975) Construction and optimality of generalised Youden designs. A survey of statistical design and linear models. J N Srivastava Edited, pp 353
Mukhopadhyay Sunanda (1981) On the optimality of block designs under mixed effects model. Cal Stat Assoc Bull 30:171
Takeuchi K (1961) On the optimality of certain types of PBIB design. Rep Statist Appl Res Un Japan Sci, Engrs B 3:140
Takeuchi K (1963) A remark added to “On the optimality of certain type of PBIB designs”. Rep Statist Appl Res JUSE 10:47
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Bagchi, S. On theE-optimality of certain asymmetrical designs under mixed effects model. Metrika 34, 95–105 (1987). https://doi.org/10.1007/BF02613134
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DOI: https://doi.org/10.1007/BF02613134