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
- 在一般混合方差分析模型中，如何获得计算方便的方差分量估计，并确定其在特定正态与非正态情形下的效率性质？
- 方法与思路
- 作者令先验方差与先验误差方差之比相同并趋于无穷，得到不变二次无偏估计，研究其效率极限并提供计算公式。
- 材料陈述的贡献
- 摘要称正态下真方差比相同且趋于无穷时相对 MIVQUE 效率趋一；非正态两分量模型在类数和每类观测数增大时具有渐近有效性。
- 阅读关注点
- 应区分先验比率构造与真方差比率条件，核对双重增长的设计序列、最优性比较类，以及不平衡模型中的计算复杂度。
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- 仅据 OpenAlex 索引摘要，稿件版本未注明；最优性限于指定分布、比率与渐近设计，不能解释为任意混合模型中的效率优势。
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).