Approximate solutions for the maximum-likelihood estimates in models of univariate human twin data

We present numerical results concerning the accuracy of approximate maximum-likelihood estimators of variance components for several models of univariate human twin data. The approximations are obtained via a spectral decomposition of the twin model covariance matrix. The results apply to likelihood functions for univariate twin data based on either the Wishart distribution or the bivariate normal distribution. For sample sizes of 100 twin pairs for each zygosity group, if the difference of the traces of the sample covariance matrices is 10% or less of the sum of the traces, the approximate solutions can be used as the maximum-likelihood estimators for some models.