Computable MINQUE-Type Estimates of Variance Components
可计算的 MINQUE 型方差分量估计AI 解读 ↓
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可计算的 MINQUE 型方差分量估计
- 研究问题
- 在混合方差分析模型中，如何构造计算方便的方差分量估计，并研究其在正态与非正态随机效应下的效率？
- 方法与思路
- 作者令各先验方差与先验误差方差的比值相同，再让共同比值趋于无穷，得到不变二次无偏估计并给出计算公式。
- 材料陈述的贡献
- 摘要称，正态情形下特定方差比极限中相对效率趋于一；两方差分量非正态模型中，特定设计序列下达到渐近效率。
- 阅读关注点
- 应核对两类效率结论各自的分布与设计条件、非平衡模型中的方差比较，以及一般混合模型计算公式的适用范围。
- 阅读边界
- 所给索引摘要未标稿件版本。效率结论依赖特定极限，摘要未列完整正则条件，不能推广为所有设计下的有限样本优势。
原文摘要
The minimum norm quadratic unbiased estimator type (MINQUE type) of estimates considered in this article are obtained by requiring identical values for the ratios of the a priori variances to the a priori error variance and letting this common value tend to infinity. The resulting estimates are invariant quadratic unbiased estimators with certain parametric and nonparametric optimality properties: assuming normally distributed random effects the efficiency of the proposed estimates to the minimum variance quadratic unbiased estimates (MIVQUE's) approaches unity when the true variance ratios are identical and tend to infinity. Assuming nonnormal effect distributions in the model with two variance components, the estimates are asymptotically efficient: in a sequence of designs where the number of classes and the number of observations on each class approach infinity, it is shown that the asymptotic variances of the estimates are equivalent to the theoretical minimum variances for invariant quadratic unbiased estimators. The result is interesting and useful since the usual analysis of variance (ANOVA) estimate of between-classes variance has strictly larger asymptotic variance for the unbalanced one-way model. Commonly considered estimates result from this procedure; the usual residual mean square (assuming that all non-error effects are fixed) is the resulting estimate of the error variance. In the one-way model the resulting estimates coincide with estimates considered by Thomas and Hultquist (1978), Burdick and Graybill (1984), Ahrens, Kleffe, and Tenzler (1981), and Kaplan (1982). In particular, the convergence of the MINQUE estimates was proved in the latter two papers in the context of the unbalanced one-way model. The procedure yields computationally convenient estimates in the general mixed ANOVA model. Computing formulas are given, and it is noted that the computational complexity of these estimates is comparable with the computational complexity of a special case of MINQUE demonstrated by Wansbeek (1980).