SIMULTANEOUS ESTIMATION OF SEVERAL INTRACLASS CORRELATION COEFFICIENTS

S. E. AHMED^{1} , A. K. GUPTA^{2}, S. M. KHAN^{1} AND C. J. NICOL^{3}

1Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan,

Canada S4S 0A2, e-mail: ahmed@albiruni.math.uregina.ca

2Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, U.S.A.

3Department of Economics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

(Received January 30, 1995; revised December 27, 1999)

Abstract. Based on shrinkage and preliminary test rules, various estimators are proposed for estimation of several intraclass correlation coefficients when independent samples are drawn from multivariate normal populations. It is demonstrated that the James-Stein type estimators are asymptotically superior to the usual estimators. Furthermore, it is also indicated through asymptotic results that none of the preliminary test and shrinkage estimators dominate each other, though they perform relatively well as compared to the classical estimator. The relative dominance picture of the estimators is presented. A Monte Carlo study is performed to appraise the properties of the proposed estimators for small samples.

Key words and phrases: Paired estimation, intraclass correlation coefficients, asymptotic distributional risk, shrinkage estimators and preliminary test, local alternatives, Monte Carlo, maximum likelihood estimation.