Comparison of recent estimators of interclass correlation from familial data

The asymptotic and finite-sample properties of several recent estimators of interclass correlation are compared to more traditional estimators in the case of a variable number of siblings per family. It is shown that Karlin's family-weighted pairwise estimator (Karlin, Cameron, and Williams, 1981, Proceedings of the National Academy of Science 78, 2664-2668) is virtually equivalent to the ensemble estimator (Rosner, Donner, and Hennekens, 1977, Applied Statistics 26, 179-187), thus suggesting an estimator of the former's asymptotic variance. Further, an estimator proposed by Srivastava (1984, Biometrika 71, 177-185) is shown to be identical to the modified sib-mean estimator (Konishi, 1982, Annals of the Institute of Statistical Mathematics 34, 505-515) when the sib-sib correlation is estimated by the method of unweighted group means. Although the estimator due to Srivastava has smaller asymptotic variance than the other two, the gain in efficiency is slight, for familial data, both asymptotically and in finite samples.