On Combining Information in Generally Balanced Nested Block Designs

References

• Bailey , R. A. ( 1994 ). General balance: artificial theory or practical relevance? . In: Caliński , T. , Kala , R. , Eds., Proc. International Conference on Linear Statistical Inference LINSTAT’93 . Dordrecht : Kluwer Academic Publishers , pp. 171 – 184 .
   Google Scholar
• Bailey , R. A. ( 1999 ). Choosing designs for nested blocks . Listy Biometryczne—Biometr. Lett. 36 : 85 – 126 .
   Google Scholar
• Bogacka , B. , Mejza , S. ( 1994 ). Optimality of generally balanced experimental block designs . In: Caliński , T. , Kala , R. , Eds., Proc. International Conference on Linear Statistical Inference LINSTAT’93 . Dordrecht : Kluwer Academic Publishers , pp. 185 – 194 .
   Google Scholar
• Bose , R. C. ( 1942 ). A note on the resolvability of balanced incomplete block designs . Sankhy 6 : 105 – 110 .
   Google Scholar
• Caliński , T. ( 1994 ). On the randomization theory of experiments in nested block designs . Listy Biometryczne—Biometr. Lett. 31 : 45 – 77 .
   Google Scholar
• Caliński , T. ( 1997 ). Recovery of inter-block information when the experiment is in a nested block design . Listy Biometryczne—Biometr. Lett. 34 : 9 – 26 .
   Google Scholar
• Caliński , T. , Kageyama , S. ( 2000 ). Block Designs: A Randomization Approach, vol. I: Analysis . Lecture Notes in Statistics , vol. 150. New York : Springer .
   Google Scholar
• Caliński , T. , Kageyama , S. ( 2008 ). On the analysis of experiments in affine resolvable designs . J. Statist. Plann. Infer. 138 : 3350 – 3356 .
   Web of Science ®Google Scholar
• Caliński , T. , Czajka , S. , Pilarczyk , W. (2009). On the application of affine resolvable designs to variety trials. J. Statist. Applic. 4:33–56.
   Google Scholar
• Harville , D. A. , Jeske , D. R. ( 1992 ). Mean squared error of estimation or prediction under a general linear model . J. Amer. Statist. Assoc. 87 : 724 – 731 .
   Web of Science ®Google Scholar
• Houtman , A. M. , Speed , T. P. ( 1983 ). Balance in designed experiments with orthogonal block structure . Ann. Statist. 11 : 1069 – 1085 .
   Web of Science ®Google Scholar
• Kackar , R. N. , Harville , D. A. ( 1984 ). Approximations for standard errors of estimators of fixed and random effects in mixed linear models . J. Amer. Statist. Assoc. 79 : 853 – 862 .
   Web of Science ®Google Scholar
• Kageyama , S. ( 1972 ). A survey of resolvable solutions of balanced incomplete block designs . Int. Statist. Rev. 40 : 269 – 273 .
   Web of Science ®Google Scholar
• Kempthorne , O. ( 1952 ). The Design and Analysis of Experiments . New York : Wiley .
   Google Scholar
• Kuriki , S. , Mejza , I. , Mejza , S. ( 2012 ). Incomplete split-plot designs supplemented by a single control . Commun. Statist. Theor. Meth. 41 : 2490 – 2502 .
   Web of Science ®Google Scholar
• Mejza , S. , Kageyama , S. ( 1995 ). On the optimality of certain nested block designs under a mixed effects model . In: Kitsos , C. P. , Müller , W. G. , Eds., Moda 4—Advances in Model-Oriented Data Analysis . Heidelberg : Physica-Verlag , pp. 157 – 164 .
   Google Scholar
• Mejza , S. , Kageyama , S. ( 1998 ). Some statistical properties of nested block designs . In: Atkinson , A. C. , Pronzato , L. , Wynn , H. P. , Eds., Moda 5—Advances in Model-Oriented Data Analysis and Experimental Design . Heidelberg : Physica-Verlag , pp. 231 – 238 .
   Google Scholar
• Moreira , E. , Mexia , J. T. , Fonseca , M. , Zmyślony , R. ( 2009 ). L models and multiple regressions designs . Statist. Pap. 50 : 869 – 885 .
   Web of Science ®Google Scholar
• Nelder , J. A. ( 1954 ). The interpretation of negative components of variance . Biometrika 41 : 544 – 548 .
   Web of Science ®Google Scholar
• Nelder , J. A. ( 1965 ). The analysis of randomized experiments with orthogonal block structure . Proc. Roy. Soc. Lond. Ser. A 283 : 147 – 178 .
   Web of Science ®Google Scholar
• Nelder , J. A. ( 1968 ). The combination of information in generally balanced designs . J. Roy. Statist. Soc. Ser. B 30 : 303 – 311 .
   Google Scholar
• Neyman , J. ( 1935 ), with cooperation of K. Iwaszkiewicz and S. Kołodziejczyk. Statistical problems in agricultural experimentation (with discussion) . J. Roy. Statist. Soc. Suppl . 2 : 107 – 180 .
   Google Scholar
• Patterson , H. D. , Thompson , R. ( 1975 ). Maximum likelihood estimation of components of variance . In: Corsten , L. C. A. , Postelnicu , T. , Eds., Proc. 8th International Biometric Conference . Bucuresti : Editura Academiei , pp. 197 – 207 .
   Google Scholar
• R Development Core Team ( 2010 ). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. URL http://www.r-project.org .
   Google Scholar
• Rao , C. R. ( 1979 ). MINQUE theory and its relation to ML and MML estimation of variance components . Sankhy Ser. B 41 : 138 – 153 .
   Google Scholar
• Rao , C. R. , Kleffe , J. ( 1988 ). Estimation of Variance Components and Applications . Amsterdam : North-Holland .
   Google Scholar
• Shrikhande , S. S. , Raghavarao , D. ( 1964 ). Affine α-resolvable incomplete block designs . In: Rao , C. R. , Ed., Contributions to Statistics . Calcutta : Pergamon Press, Statistical Publishing Society , pp. 471 – 480 .
   Google Scholar
• Yates , F. ( 1940 ). Lattice squares . J. Agric. Sci. 30 : 672 – 687 .
   Google Scholar