The Michigan Mathematical Journal

Variance and concurrence in block designs, and distance in the corresponding graphs

R. A. Bailey

Full-text: Open access

Article information

Source
Michigan Math. J. Volume 58, Issue 1 (2009), 105-124.

Dates
First available in Project Euclid: 11 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1242071685

Digital Object Identifier
doi:10.1307/mmj/1242071685

Mathematical Reviews number (MathSciNet)
MR2526080

Zentralblatt MATH identifier
1185.05016

Subjects
Primary: 62K10: Block designs 05B05: Block designs [See also 51E05, 62K10] 05C12: Distance in graphs
Secondary: 51E05: General block designs [See also 05B05] 05E30: Association schemes, strongly regular graphs

Citation

Bailey, R. A. Variance and concurrence in block designs, and distance in the corresponding graphs. Michigan Math. J. 58 (2009), no. 1, 105--124. doi:10.1307/mmj/1242071685. https://projecteuclid.org/euclid.mmj/1242071685


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References

  • B. Bagchi and S. Bagchi, Optimality of partial geometric designs, Ann. Statist. 29 (2001), 577--594.
  • R. A. Bailey, Association schemes. Designed experiments, algebra and combinatorics, Cambridge Stud. Adv. Math., 84, Cambridge Univ. Press, Cambridge, 2004.
  • ------, Designs for two-colour microarray experiments, J. Roy. Statist. Soc. Ser. C 56 (2007), 365--394.
  • R. A. Bailey, P. J. Cameron, P. Dobcsányi, J. P. Morgan, and L. H. Soicher, Designs on the web, Discrete Math. 306 (2006), 3014--3027.
  • R. A. Bailey, H. Monod, and J. P. Morgan, Construction and optimality of affine-resolvable designs, Biometrika 82 (1995), 187--200.
  • R. C. Bose and K. R. Nair, Partially balanced incomplete block designs, Sankhy\B a 4 (1939), 337--372.
  • ------, Resolvable incomplete block designs with two replications, Sankhy\B a Ser. A 29 (1962), 9--24.
  • R. C. Bose and T. Shimamoto, Classification and analysis of partially balanced incomplete block designs with two associate classes, J. Amer. Statist. Assoc. 47 (1952), 151--184.
  • A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-regular graphs, Ergeb. Math. Grenzgeb. (3), 18, Springer-Verlag, Berlin, 1989.
  • C.-S. Cheng, Optimality of certain asymmetrical experimental designs, Ann. Statist. 6 (1978), 1239--1261.
  • ------, On the $E$-optimality of some block designs, J. Roy. Statist. Soc. Ser. B 42 (1980), 199--204.
  • C.-S. Cheng and R. A. Bailey, Optimality of some two-associate-class partially balanced incomplete-block designs, Ann. Statist. 19 (1991), 1667--1671.
  • E. R. van Dam, Regular graphs with four eigenvalues, Linear Algebra Appl. 226/228 (1995), 139--162.
  • R. A. Fisher, Statistical methods for research workers, Oliver & Boyd, Edinburgh, 1925.
  • C. D. Godsil and B. D. McKay, Feasibility conditions for the existence of walk-regular graphs, Linear Algebra Appl. 30 (1980), 51--61.
  • Ja. Ju. Gol'fand, A. V. Ivanov, and M. H. Klin, Amorphic cellular rings, Investigations in algebraic theory of combinatorial objects (I. A. Farad\uzev, A. A. Ivanov, M. H. Klin, A. J. Woldar, eds.), Math. Appl. (Soviet Ser.), 84, pp. 167--187, Kluwer, Dordrecht, 1994.
  • D. G. Higman, Combinatorial considerations about permutation groups, Mathematical Institute, Oxford, 1971.
  • D. R. Hughes, Combinatorial analysis: $t$-designs and permutation groups, Proc. Sympos. Pure Math., 6, pp. 39--41, Amer. Math. Soc., Providence, RI, 1962.
  • M. Jacroux, On the $E$-optimality of regular graph designs, J. Roy. Statist. Soc. Ser. B 42 (1980), 205--209.
  • ------, Some minimum variance block designs for estimating treatment differences, J. Roy. Statist. Soc. Ser. B 45 (1983), 70--76.
  • A. T. James and G. N. Wilkinson, Factorization of the residual operator and canonical decomposition of nonorthogonal factors in the analysis of variance, Biometrika 58 (1971), 279--294.
  • R. G. Jarrett, Definitions and properties for $m$-concurrence designs, J. Roy. Statist. Soc. Ser. B 45 (1983), 1--10.
  • B. Jin and J. P. Morgan, Optimal saturated block designs when observations are correlated, J. Statist. Plann. Inference 38 (2008), 3299--3308.
  • J. A. John, Cyclic designs, Monogr. Statist. Appl. Probab., Chapman & Hall, London, 1987.
  • J. A. John and T. Mitchell, Optimal incomplete block designs, J. Roy. Statist. Soc. Ser. B 39 (1977), 39--43.
  • B. Jones and J. A. Eccleston, Exchange and interchange procedures to search for optimal designs, J. Roy. Statist. Soc. Ser. B 42 (1980), 238--243.
  • O. Kempthorne, The efficiency factor of an incomplete-block design, Ann. Math. Statist. 27 (1956), 846--849.
  • M. K. Kerr and G. A. Churchill, Experimental design for gene expression microarrays, Biostatistics 2 (2001), 183--201.
  • A. M. Kshirsagar, A note on incomplete block designs, Ann. Math. Statist. 29 (1958), 907--910.
  • J. Kunert, Optimal experimental design when the errors are assumed to be correlated, Statist. Decisions, suppl. 2 (1985), 287--298.
  • R. Mead, The non-orthogonal design of experiments, J. Roy. Statist. Soc. Ser. A 153 (1990), 151--178.
  • J. P. Morgan, Optimal incomplete block designs, J. Amer. Statist. Assoc. 102 (2007), 655--663.
  • V. L. Mote, On a minimax property of a balanced incomplete block design, Ann. Math. Statist. 29 (1958), 910--913.
  • L. J. Paterson, Circuits and efficiency in incomplete block designs, Biometrika 70 (1983), 215--225.
  • K. R. Shah and B. K. Sinha, Theory of optimal designs, Lecture Notes in Statist., 54, Springer-Verlag, New York, 1989.
  • B. K. Sinha, Some aspects of simplicity in the analysis of block designs, J. Statist. Plann. Inference 6 (1982), 165--172.
  • E. R. Williams, A note on rectangular lattice designs, Biometrics 33 (1977), 410--414.
  • E. R. Williams, H. D. Patterson, and J. A. John, Resolvable designs with two replications, J. Roy. Statist. Soc. Ser. B 38 (1976), 296--301.
  • ------, Efficient two-replicate resolvable designs, Biometrics 33 (1977), 713--717.
  • E. Wit, A. Nobile, and R. Khanin, Near-optimal designs for dual channel microarray studies, J. Roy. Statist. Soc. Ser. C 54 (2005), 817--830.
  • F. Yates, Incomplete randomized blocks, Ann. Eugenics 7 (1936), 121--140.
  • ------, A new method for arranging variety trials involving a large number of varieties, J. Agric. Sci. 26 (1936), 424--455.