Existence conditions for the uniformly minimum risk unbiased estimators in a class of linear models

This paper studies the existence of the uniformly minimum risk unbiased (UMRU) estimators of parameters in a class of linear models with an error vector having multivariate normal distribution or t-distribution, which include the growth curve model, the extended growth curve model, the seemingly unrelated regression equations model, the variance components model, and so on. The necessary and sufficient existence conditions are established for UMRU estimators of the estimable linear functions of regression coefficients under convex losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model with normality assumption, the conclusions given in the literature can be derived by applying the general results in this paper. For the variance components model, the necessary and sufficient existence conditions are reduced as terse forms.