C. R. Henderson, the Statistician; and His
Contributions to Variance Components Estimation
Searle SR
Biometrics Unit, Cornell University, Ithaca, NY 14853.
Journal of Diary Science , 74(11):4035-4044 (1991)
Abstract
C. R. Henderson's 1953 Biometrics paper "Estimation of Variance and Covariance
Components" 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.
Variance component linkage analysis