Nonlinear, biased estimators and predictors of the James-Stein form are compared numerically with ML estimation of fixed effects and BLUP prediction. At least in some situations considered, it appears that considerable improvement can be achieved in terms of conditional mean squared error and conditional absolute error. The possibility of improving upon REML using Bayesian methods is raised. Methods for deriving the exact posterior distribution of heritability in an animal model and either exact or approximate marginal posterior distributions of variance components are discussed. 

Daniel Gianola

Proceedings of the World Congress on Genetics Applied to Livestock Production, Volume XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation., , 445–449, 1990
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