Statistical Analysis of Nonrectangular Family Data

MINQUE (Minimum Norm Quadratic Unbiased Estimators) theory is applied to the problem of estimation of variance components in family data (siblings) with variable family size. Using this approach, the traditional iterative maximum likelihood estimators are shown to be asymptotically normal, even though the data come from non‐identical parent distributions. Asymptotic expressions are also obtained for the variance of the MINQUE estimators which hold even if the data are decidedly non‐normal (e.g. a mixture of normals). In the case of normal data, exact small‐sample variance estimates are derived. Simulations demonstrate the fast rate of convergence to asymptotic properties as the number of families increases. These desirable qualities suggest that the easy to compute MINQUE class of estimators may provide a useful alternative method for modelling familial aggregation.