C. R. Henderson, the Statistician; And His Contributions to Variance Components Estimation

Abstract

C. R. Henderson's 1953 Biometrics paper “Estimation of Variance and Covariance Components” (25) is an outstanding landmark in the discipline of statistics. It sets out the very first ideas of how to estimate variance components from unbalanced (unequal subclass numbers) data in situations more complicated than the one-way classification (completely randomized design). As such it had three important, long-lasting impacts. First, it provided methods for actually using unbalanced data, even in large quantity, for estimating variance components. And this has played a tremendous role in population genetics and in animal breeding where the use of estimated variance components is vital to the application of selection theory and selection index techniques. Second, that 1953 paper stimulated numerous statisticians to become interested in random effects, mixed models, and variance components estimation, with such statistical greats as H. O. Hartley and C. R. Rao making contributions in the late 1960s and early 1970s. By then, improved methods of estimating variance components from unbalanced data had been developed, namely maximum likelihood (ML) and restricted maximum likelihood (REML). Once computing power had expanded to the point where these methods became feasible, Henderson made notable contributions to these methods, allied to his two great interests: animal breeding and feasible computing procedures. For both of these, his mixed model equations were a salient feature. Third, these methods reached a wide audience of geneticists and statisticians.