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On theE-optimality of certain asymmetrical designs under mixed effects model

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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.

  1. i)

    A group divisible design with λ2 = λ1 + 1.

  2. ii)

    A group divisible design with λ1 = λ2 + 1 and group size 2.

  3. iii)

    A linked block design.

  4. iv)

    The dual of design (i)

  5. 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

    MATH  MathSciNet  Google Scholar 

  • Cheng CS (1980) On theE-optimality of some block designs. Jour Roy Stat Soc 13/42:199

    Google Scholar 

  • Constantine GM (1981) SomeE-optimal block designs. Ann Statist 9:886

    MATH  MathSciNet  Google Scholar 

  • Jacroux M (1980) On theE-optimality of regular graph designs. Jour Roy Stat Soc B 42:205

    MATH  MathSciNet  Google Scholar 

  • John JA, Mitchell TJ (1977) Optimal incomplete block designs. Jour Roy Soc B:29

    Google Scholar 

  • 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

    MATH  Google Scholar 

  • Takeuchi K (1961) On the optimality of certain types of PBIB design. Rep Statist Appl Res Un Japan Sci, Engrs B 3:140

    Google Scholar 

  • Takeuchi K (1963) A remark added to “On the optimality of certain type of PBIB designs”. Rep Statist Appl Res JUSE 10:47

    Google Scholar 

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Authors and Affiliations

  1. Mukhopadhyay

    S. Bagchi

  2. Computer Science Unit, Indian Statistical Institute, 203, B.T. Road, 700035, Calcutta, India

    S. Bagchi

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  1. S. Bagchi
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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

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