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Optimal properties of the conditional mean as a selection criterion
1Department of Animal Sciences, University of Illinois, 61801, Urbana, IL, USA.
Summary
Optimal candidate selection involves using conditional means for constant proportions, ensuring maximum expected merit. This method is distribution-independent but requires adjustments for random proportions or varying expected merit.
Area of Science:
- Statistics
- Quantitative Genetics
- Biometry
Background:
- Candidate selection aims to maximize expected merit.
- Traditional methods may not be optimal under all conditions.
Purpose of the Study:
- To discuss rules for selection that maximize expected merit.
- To identify optimal selection strategies regardless of data distribution.
Main Methods:
- Selection based on conditional means of merit given observations.
- Utilizing a vector of "corrected" records (w) when expected values are linear functions of parameters.
- Applying Best Linear Unbiased Prediction (BLUP) under normality assumptions.
Main Results:
- Conditional means provide optimum selection for constant proportions, irrespective of distribution.
- Selection rules require modification if the proportion selected is random.
- BLUP is identified as the optimal rule under normality when expected merit is constant across candidates.
Conclusions:
- Conditional mean-based selection is robust for constant proportions.
- BLUP is justified for selection when expected merit varies, using a Bayesian approach.
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