Bayes estimates in one-way and two-way models
Bayes estimates in one-way and two-way models
复制标题
单向和双向模型中的贝叶斯估计
DOI：
10.1093/biomet/60.2.319
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发表时间：
1973
期刊：
影响因子：
2.7
通讯作者：
A. Smith
中科院分区：
文献类型：
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作者：
A. Smith
其中y是n×1，Oi是pi x 1(i=1，2，3)，并且适当地标注了{Ai}和{Ci}的尺寸。Smith(1973)得到了由这种结构得到的估计量的一些一般性质，特别是研究了兴趣集中在02的情况；这对应于经典的模型II的情况。在这篇文章中，我们主要关注在上述结构被用来结合在典型试验设计情况下可能获得的有意义的先验的情况下，01的估计：2讨论了两种这样的形式，可交换先验和响应面先验。在(1)-(3)中已知协方差结构的假设下，？3和4中我们分别在单向设计和双向设计中使用这些先验来获得均值的新估计；？5去掉了这一明显不切实际的假设。数值算例见？6。
where y is n x 1, Oi is pi x 1 (i = 1, 2, 3), and {Ai} and {Ci} are appropriately dimensioned. Smith (1973) obtained some general properties of estimators derived from this structure, and, in particular, investigated the case where interest centres on 02; this corresponds to the classical model II situation. In this paper we are concerned primarily with the estimation of 01 in cases where the above structure is used to incorporate meaningful priors that might obtain in typical experimental design situations: ? 2 discusses two such forms, exchangeable priors and response-surface priors. In ??3 and 4 we use these priors to obtain new estimates of the means in one-way and two-way designs, respectively, under the assumption that the covariance structure is known in (1)-(3); ? 5 removes this obviously unrealistic assumption. Numerical examples are provided in ? 6.