A derivation of BLUP - Best linear unbiased predictor

Statistics and Probability Letters

Volumn 32, Issue 3, 1997, Pages 321-324

  Jiang, Jiming ^a  

^a CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

Error contrasts; Mixed models; REML

Indexed keywords

EID: 0031569127     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(96)00089-2     Document Type: Article

References (17)

1. Bulmer, M.G. (1980), The Mathematical Theory of Quantitative Genetics (Oxford University Press, Oxford).
2. Dempfle, L. (1977), Relation entre BLUP (best linear unbiased prediction) et estimateurs Bayesiens, Ann. Genetique Selection Animale 9, 27-32.
3. Gianola, D. and B. Goffinet (1982), Sire evaluation with best linear predictors, Biometrics 38, 1085-1088.
4. Fellner, W.H. (1986), Robust estimation of variance components, Technometrics 28, 51-60.
5. Harville, D.A. (1976), Extension of the Gauss-Markov theorem to include the estimation of random effects, Ann. Statist. 4, 384-395.
6. Harville, D.A. (1977), Maximum likelihood approaches to variance component estimation and to related problems, J. Amer. Statist. Assoc. 72, 320-340.
7. Harville, D.A. (1990), BLUP (Best linear unbiased prediction) and beyond, in: D. Gianola and K. Hammond, eds., Advances in Statistical Methods for Genetic Improvement of Livestock (Springer, New York) pp. 239-276.
8. Henderson, C.R. (1950), Estimation of genetic parameters (abstract), Ann. Math. Statist. 21, 309-310.
9. Henderson, C.R. (1963), Selection index and expected genetic advance, in: Statistical Genetics and Plant Breeding, pp. 141-163, Nat. Acad. Sci., Nat. Res. Council, Publication 982, Washington, DC.
10. Jiang, J. (1996), REML estimation: asymptotic behavior and related topics, Ann. Statist. 24, 255-286.
11. Lindley, D.V. and A.F.M. Smith (1972), Bayes estimates for the linear model (with discussion), J. Roy. Statist. Soc. Ser. B 34, 1-41.
12. Patterson, H.D. and R. Thompson (1971), Recovery of interblock information when block sizes are unequal, Biometrika 58, 545-554.
13. Rao, C.R. and J. Kleffe (1988), Estimation of Variance Components and Applications (North-Holland, Amsterdam).
14. Robinson, G.K. (1991), That BLUP is a good thing: the estimation of random effects, Statist. Sci. 6, 15-51.
15. Searle, S.R., G. Casella and C.E. McCulloch (1992), Variance Components (Wiley, New York).
16. Speed, T. (1991), Comment on Robinson: estimation of random effects, Statist. Sci. 6, 42-44.
17. Thompson, R. (1980), Maximum likelihood estimation of variance components, Math. Operforsh, Statist. Ser. Statist. 11, 545-561.