Estimation of parent-offspring correlation

When families have different numbers of offspring, Srivastava (1984) provided an easily computable estimator as an alternative to the maximum likelihood estimator of parent-offspring correlation. Some properties of this estimator are discussed vis-à-vis with those of ensemble and pairwise estimators. Further, we derive the small sample distribution of Srivastava's estimator under the assumption of null parent-offspring correlation. In the process, we demonstrate that a certain function of the classical sib-mean estimator has Student's t distribution despite differing sib-ship sizes.