K. Meyer et Sp. Smith, RESTRICTED MAXIMUM-LIKELIHOOD-ESTIMATION FOR ANIMAL-MODELS USING DERIVATIVES OF THE LIKELIHOOD, Genetics selection evolution, 28(1), 1996, pp. 23-49
Restricted maximum likelihood estimation using first and second deriva
tives of the likelihood is described. It relies on the calculation of
derivatives without the need for large matrix inversion using an autom
atic differentiation procedure. In essence, this is an extension of th
e Cholesky factorisation of a matrix. A reparameterisation is used to
transform the constrained optimisation problem imposed in estimating c
ovariance components to an unconstrained problem, thus making the use
of Newton-Raphson and related algorithms feasible. A numerical example
is given to illustrate calculations. Several modified Newton-Raphson
and method of scoring algorithms are compared for applications to anal
yses of beef cattle data, and contrasted to a derivative-free algorith
m.