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The method is an old one but is described in one of these papers. Dodenhoff is the visiting fellow who added it to MTDFREML. The method is often referenced in statistics as the 'delta' method.
Dodenhoff, J., L.D. Van Vleck,S.D. Kachman, and R.M. Koch. 1998. Parameter estimates for direct, maternal and grandmaternal genetic effects for birth weight and weaning weight in Hereford cattle. J. Anim. Sci. 76:2521-2527.
Dodenhoff, J., L.D. Van Vleck, and D.E. Wilson. 1999. Comparison of models to estimate genetic effects for weaning weight of Angus cattle. J. Anim. Sci. 77:3176-3184.
In addition, the slides contained in Kachman-SE.pptx describes modifications needed for the data file to obtain SE of estimates of genetic parameters for multiple trait analyses when all animals do not have all traits measured. When the slides were prepared the paper had not been published. It has now been published as a technical note: Kachman, S.D. and L.D. Van Vleck. 2007. Technical Note: Calculation of standard errors of estimates of genetic parameters with the multiple-trait derivative-free restricted maximal likelihood programs. J. Anim. Sci. 85: 2375–2381.