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Cross-validation tools are used increasingly to validate and compare genetic evaluation methods but analytical properties of cross-validation methods are rarely described. There is also a lack of cross-validation tools for complex problems such as prediction of indirect effects (e.g. maternal effects) or for breeding schemes with small progeny group sizes.

We derive the expected value of several quadratic forms by comparing genetic evaluations including “partial” and “whole” data. We propose statistics that compare genetic evaluations including “partial” and “whole” data based on differences in means, covariance, and correlation, and term the use of these statistics “method LR” (from linear regression). Contrary to common belief, the regression of true on estimated breeding values is (on expectation) lower than 1 for small or related …