Simulation studies are used to explore the properties of procedures for estimating components of variance and constructing test statistics in genetic linkage studies of quantitative traits. We evaluated the bias and median squared error of estimates of the linked additive genetic variance obtained by regression, maximum likelihood and quasilikelihood estimation procedures. The quasilikelihood and regression procedures provided unbiased estimates of the additive component of variance. Maximum likelihood procedures that assumed multivariate normality were biased for most sample sizes considered but had more precision for most generating models than regression or quasilikelihood methods did. Wald tests derived from quasilikelihood procedures had similar or greater power than Wald tests based upon estimators from maximum likelihood analyses. Quasilikelihood estimation may therefore be preferable whenever there is uncertainty about the generating distribution for the error variance, but the robustness of this approach is offset by its required computational complexity.