A simulation study examining the effects of 'regularization' on estimates of genetic covariance matrices for small samples is presented. This is achieved by penalizing the likelihood, and three types of penalties are examined. It is shown that regularized estimation can substantially enhance the accuracy of estimates of genetic parameters. Penalties shrinking estimates of genetic covariances or correlations towards their phenotypic counterparts acted somewhat differently to those aimed reducing the spread of sample eigenvalues. While improvements of estimates were found to be comparable overall, shrinkage of genetic towards phenotypic correlations resulted in least bias.

Multivariate estimation fitting a common structure to estimates of genetic and environmental covariance matrices is examined in a simple simulation study. It is shown that such parsimonious estimation can considerably reduce sampling variation. However, if the assumption of similarity in structure does not hold at least approximately, bias in estimates of the genetic covariance matrix can be substantial. For small samples and more than a few traits, structured estimation is likely to reduce mean square error even if bias is quite large. Hence such models should be used cautiously.