Balance and orthogonality in designs for mixed classification models

Annals of Statistics

Volumn 27, Issue 6, 1999, Pages 1927-1947

  Vanleeuwen, Dawn M ^a   Birkes, David S ^a   Seely, Justus F ^a  

^a NONE

Author keywords

ANOVA; Mixed linear model; Orthogonal block structure; Orthogonal design; Sums of squares

Indexed keywords

EID: 0033234639     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. BROWN, K. G. (1983). Sub-balanced data and the mixed analysis of variance. J. Amer. Statist. Assoc. 78 162-167.
2. EL-BASSIOUNI, M. Y. (1983). On the existence of explicit restricted maximum likelihood estimators in multivariate normal models. Sankhyā Sur. B 42 1069-1085.
3. EL-BASSIOUNI, M. Y. and SEELY, J. (1980). Optimal tests for certain functions of the parameters in a covariance matrix with linear structure. Sankhyā Ser. A 42 64-77.
4. HOUTMAN, A. M. and SPEED, T. P. (1983). Balance in designed experiments with orthogonal block structure. Ann. Math. Statist. 42 1069-1085.
5. NELDER, J. A. (1965). The analysis of randomized experiments with orthogonal block structure I. Block structure and the null analysis of variance. Proc. Roy. Soc. London Ser. A 273 147-162.
6. PUKELSHEIM, F. (1981). On the existence of unbiased nonnegative estimates of variance covariance components. Ann. Statist. 9 293-299.
7. PUKELSHEIM, F. (1993). Optimal Design of Experiments. Wiley, New York.
8. RAO, C. R. and KLEFFE, J. (1988). Estimation of Variance Components and Applications. North-Holland, New York.
9. SEELY, J. (1971). Quadratic subspaces and completeness. Ann. Math. Statist. 42 710-721.
10. SEELY, J. (1972). Completeness for a family of multivariate normal distributions. Ann. Math. Statist. 43 1644-1647.
11. SEELY, J. (1977). Minimal sufficient statistics and completeness for multivariate normal families. Sankhyā Ser. A 39 170-185.
12. SEIFERT, B. (1979). Optimal testing for fixed effects in general balanced mixed classification models. Math. Operationsforsch. Statist. Ser. Statist. 10 237-255.
13. SZATROWSKI, T. H. (1980). Necessary and sufficient conditions for explicit solutions in the multivariate normal estimation problem for patterned means and covariances. Ann. Statist. 8 802-810.
14. VANLEEUWEN, D. M., BIRKES, D. S. and SEELY, J. F. (1997). Balance and orthogonality in designs for mixed classification models. Technical Report 168, Dept. Statistics, Oregon State Univ.
15. VANLEEUWEN, D. M., SEELY, J. F. and BIRKES, D. S. (1998). Sufficient conditions for orthogonal designs in mixed linear models. J. Statist. Plann. Inference 73 373-389.