# That BLUP is a Good Thing: The Estimation of Random Effects

@article{Robinson1991ThatBI, title={That BLUP is a Good Thing: The Estimation of Random Effects}, author={G. K. Robinson}, journal={Statistical Science}, year={1991}, volume={6}, pages={15-32} }

In animal breeding, Best Linear Unbiased Prediction, or BLUP, is a technique for estimating genetic merits. In general, it is a method of estimating random effects. It can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index. It can be used for removing noise from images and for small-area estimation. This paper presents the…

## 1,682 Citations

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Unbalanced mixed linear models that contain a single set of random effects are frequently employed in animal breeding applications, in small-area estimation, and in the analysis of comparative…

### The Misuse of BLUP in Ecology and Evolution

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Analytically and through simulation and example why BLUP often gives anticonservative and biased estimates of evolutionary and ecological parameters is shown and how unbiased and powerful tests can be derived that adequately quantify uncertainty are shown.

### Performance of empirical BLUP and Bayesian prediction in small randomized complete block experiments

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SUMMARY The model for analysis of randomized complete block (RCB) experiments usually includes two factors: block and treatment. If treatment is modelled as fixed, best linear unbiased estimation…

### BLUP for phenotypic selection in plant breeding and variety testing

- BiologyEuphytica
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Recent developments in the application of BLUP in plant breeding and variety testing are reviewed, including the use of pedigree information to model and exploit genetic correlation among relatives and theUse of flexible variance–covariance structures for genotype-by-environment interaction.

### Comparison between estimation of breeding values and fixed effects using Bayesian and empirical BLUP estimation under selection on parents and missing pedigree information

- Biology, MedicineGenetics Selection Evolution
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Estimation of breeding values by Bayesian and EBLUP was similarly affected by joint effect of phenotypic or BLUP selection and randomly missing pedigree information, and bias and MSE of estimated breeding values and CG effects substantially increased across generations.

### Prediction of Complex Traits: Robust Alternatives to Best Linear Unbiased Prediction

- Medicine, MathematicsFront. Genet.
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It is presented simple (relative to a fully Bayesian analysis) to implement robust alternatives to BLUP using a linear model with residual t or Laplace distributions instead of a Gaussian one, and results obtained are encouraging and stimulate further investigation and generalization.

### Small sample inference for fixed effects from restricted maximum likelihood.

- MathematicsBiometrics
- 1997

A scaled Wald statistic is presented, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings and has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact.

### A random model approach for the LASSO

- MathematicsComput. Stat.
- 2008

Two related simulation studies are presented that show that dispersion parameter estimation results in effect estimates that are competitive with other estimation methods (including other LASSO methods).

### ESTIMATION, PREDICTION AND INFERENCE FOR THE LASSO RANDOM EFFECTS MODEL

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- 2009

The least absolute shrinkage and selection operator (LASSO) can be formulated as a random effects model with an associated variance parameter that can be estimated with other components of variance.…

### Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

- Computer Science
- 2010

An two-step algorithm is proposed for estimating the parameters, especially the variance components in the model, based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm and shown that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method.

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