Preliminary test estimators in intraclass correlation model under unequal family sizes

Abstract

The intraclass correlation model is well known in the literature of multivariate analysis and it is mainly used in studying familial data. This model is considered in this paper and the interest is focused on the estimation of the intraclass correlation on the basis of familial data from families which are randomly selected from two or more independent populations. The size of the families is considered unequal and the variances of the populations are considered unequal, too. In this statistical framework some preliminary test estimators are presented in a unified way and their asymptotic distribution is obtained. A decision-theoretic approach is developed to compare the estimators by using the asymptotic distributional quadratic risk under the null hypothesis of equality of the intraclass correlations and under contiguous alternative hypotheses, as well. Some interesting relationships are obtained between the estimators considered.