Estimation of the intraclass correlation coefficient

When families have different numbers of offspring, the maximum likelihood procedure for estimating the intraclass correlation is iterative, requiring considerable computation. Occasionally, the iterations do not even converge. To overcome this difficulty, several noniterative estimators have been proposed by Smith (1956). However, to choose from among these estimators, some prior knowledge of the intraclass correlation is needed. In this paper, a combination estimator is proposed. The asymptotic variance of this estimator is given and compared with those of the two most commonly used estimators. The comparison shows that the combination estimator always performs better than the uniform weight estimator and the loss in efficiency is not more than 7% when it is used in place of Fisher's estimator.