Pivotal estimation with applications for the intraclass correlation coefficient in the balanced one-way random effects model

In this paper pivotal quantities are used to obtain estimators of parameters. As an application of this technique, a family of estimators is presented for the intraclass correlation coefficient in the balanced one-way random effects model. The family is derived by equating a pivotal quantity to different values of the pivoting distribution, and includes the familiar REML and ML estimators. It is shown that under certain conditions, in terms of mean-squared error, most members of the family of estimators are admissible within the family. The authors provide guidance concerning the choice of an individual member of the family for estimation purposes and indicate how the method can be extended to unbalanced designs.