Is it reasonable to use of a kinship matrix for best linear unbiased prediction?

The linear mixed model (LMM) is characterized to account for the variance-covariance among entities in a population toward calculating the best linear unbiased prediction (BLUP). Animal and plant breeders widely use the LMM because it is perceived that the a BLUP estimate informs an estimated breeding value (EBV), so to speak a combining ability as a parent, obtained by relating each entity to his/her relatives using the variance-covariance. The LMM practice routinely substitutes an external kinship matrix for the variance-covariance. The challenge relevant to the LMM practice is the fact that it is unrealistic to validate the EBVs because the real breeding values are not measurable but conceptual. This unreality actually means that the EBVs are vague. Although some previous studies measured correlations between the EBVs and empirical combining abilities, they are not sufficient to remove the vagueness of EBVs because uncontrollable environmental factors might interfere with phenotypic observations for measuring the combining abilities. To overcome the challenge, this study scrutinized the soundness of the routine LMM practice from the mathematical perspective. As a result, it was demonstrated that the BLUP estimates resulting from the routine LMM practice mislead the breeding values. The genuine BLUP represents the arithmetic means of multiple phenotypic observations per each entity, given all phenotypic observations adjusted to the mean of zero.