A Simple 'Synthesis'-Based Method of Variance Component Estimation.

Abstract

An evaluation is attempted of the ever growing methodology in the estimation of variance components. Optimality properties are sometimes achieved at considerable computational efforts. Certain methods depend on a subjective ordering of the components, and if the ordering is unfortunate the method may fail to yield estimates for certain components while with a different ordering all components may well be estimable. The work involved in attempting all possible orderings of the variance components is usually prohibitive. The present method achieves optimality properties and is nevertheless computationally simple. In fact it possesses Minque optimality for a particular choice of norm, but also various other optimality properties and necessary and sufficient conditions for estimability associated with Minque simplify considerably. Moreover we are able to derive sufficient conditions for consistency which also provide estimability conditions of a simpler structure. The consistency of our estimators makes them convenient as starting points for a single ML cycle to obtain asymptotically fully efficient estimates.