Approximations for Prediction Error Variances

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Abstract
Prediction error variances and other measures of reliability of estimates of genetic merit can, in principle, be obtained by inverting matrices that arise in the estimation procedures. However, accurate inversion of these matrices would often be prohibitively expensive, and the measures of reliability do not need to be known very precisely, so approximate procedures for finding measures of reliability are often useful. Several methods for finding approximations to diagonal elements of inverses of matrices are compared and discussed. Two approximations given by VanRaden and Freeman and two new approximations are recommended for various particular applications.