Abstract
Variance component estimation, using likelihood techniques, is a nonlinear maximization problem with constraints on the solution. Iterative procedures that do not directly accommodate these constraints may have questionable statistical properties. Fast nonlinear maximizers are available, however, that maintain the solution constraints at each iteration. We apply a particular algorithm to likelihood based variance components estimation, and show that it outperforms standard procedures. established. Some algebraic reductions are also r where Y nx 1 is the vector of observations, Xnxp and Znxq L: z. are known design i=1 1 matrices, Zi having order n x qi, f3px 1 is a vector of unknown fixed effects, u = (u1,·· ·,ur) is a vector of random effects, ui having order qi X 1, and f is an n X 1 vector of random errors.
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