Estimation of Several Intraclass Correlation Coefficients

An intraclass correlation coefficient observed in several populations is estimated. The basis is a variance-stabilizing transformation. It is shown that the intraclass correlation coefficient from any elliptical distribution should be transformed in the same way. Four estimators are compared. An estimator where the components in a vector consisting of the transformed intraclass correlation coefficients are estimated separately, an estimator based on a weighted average of these components, a pretest estimator where the equality of the components is tested and then the outcome of the test is used in the estimation procedure, and a James-Stein estimator which shrinks toward the mean.