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C.R. 亨德森,这位统计学家及其对方差分量估计的贡献。

C. R. Henderson, the statistician; and his contributions to variance components estimation.

作者信息

Searle S R

机构信息

Biometrics Unit, Cornell University, Ithaca, NY 14853.

出版信息

J Dairy Sci. 1991 Nov;74(11):4035-44. doi: 10.3168/jds.S0022-0302(91)78599-8.

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.

摘要

C. R. 亨德森1953年发表在《生物统计学》上的论文《方差和协方差分量的估计》是统计学领域的一个杰出里程碑。它首次提出了在比单向分类(完全随机设计)更复杂的情况下,如何从不平衡(子类数量不等)数据中估计方差分量的想法。因此,它产生了三个重要且持久的影响。首先,它提供了实际使用不平衡数据(即使数量很大)来估计方差分量的方法。这在群体遗传学和动物育种中发挥了巨大作用,在这些领域中,估计方差分量对于选择理论和选择指数技术的应用至关重要。其次,1953年的那篇论文激发了众多统计学家对随机效应、混合模型和方差分量估计产生兴趣,像H. O. 哈特利和C. R. 拉奥这样的统计学巨匠在20世纪60年代末和70年代初做出了贡献。到那时,从不平衡数据中估计方差分量的改进方法已经得到发展,即最大似然法(ML)和限制最大似然法(REML)。一旦计算能力发展到使这些方法变得可行,亨德森就对这些方法做出了显著贡献,这与他的两大兴趣相关:动物育种和可行的计算程序。对于这两者来说,他的混合模型方程都是一个显著特征。第三,这些方法被广大遗传学家和统计学家所熟知。

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