论文信息 - Conjectures for Optimal Block Designs

Conjectures for Optimal Block Designs

SUMMARY In the study and construction of optimal block designs over the past 20 years a number of conjectures have been repeatedly stated and used. The purpose of this note is to bring together some of these conjectures. Although known to those actively engaged in research in design, it is hoped that this note will stimulate other statisticians and mathematicians to give their attention to these unsolved problems.

J. John | E. Williams

[1] K. D. Tocher. The Design and Analysis of Block Experiments , 1952 .

[2] J. Kiefer. ON THE NONRANDOMIZED OPTIMALITY AND RANDOMIZED NONOPTIMALITY OF SYMMETRICAL DESIGNS , 1958 .

[3] K. R. Shah. Optimality Criteria for Incomplete Block Designs , 1960 .

[4] J. John. Cyclic Incomplete Block Designs , 1966 .

[5] A. James,et al. Factorization of the residual operator and canonical decomposition of nonorthogonal factors in the analysis of variance , 1971 .

[6] D. Conniffe,et al. The efficiency factor of a class of incomplete block designs , 1974 .

[7] A. S. Hedayat,et al. On the Theory of Connected Designs: Characterization and Optimality , 1974 .

[8] W. H. Clatworthy,et al. Tables of two-associate-class partially balanced designs , 1975 .

[9] H. D. Patterson,et al. A new class of resolvable incomplete block designs , 1976 .

[10] C. Khatri,et al. Optimality of Two and Three Factor Designs , 1976 .

[11] Emlyn Williams,et al. Efficient Two-Replicate Resolvable Designs , 1977 .

[12] J. A. John,et al. Optimal Incomplete Block Designs , 1977 .

[13] Ching-Shui Cheng,et al. Optimality of Certain Asymmetrical Experimental Designs , 1978 .

[14] M. Jacroux,et al. On the Properties of Proper $(M, S)$ Optimal Block Designs , 1978 .

[15] Byron Jones,et al. Exchange and Interchange Procedures to Search for Optimal Designs , 1980 .

[16] M. Jacroux,et al. Some sufficient conditions for establishing (M, S)-optimality , 1980 .