Approximations for Prediction Error Variances
Geoffrey K. Robinson, L. P. Jones · Journal of Dairy Science · 1987
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.As with approximation 3, a tighter bound can be found for the particular case when the only fixed effects in the model are herd-year-seasons.This bound is approximation 6.