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混合方差分析模型中不变方差比检验的功效比较AI 解读

A class of invariant hypothesis tests is considered for the purpose of testing a variance ratio arising in mixed models. Members of the class are most powerful for specific alternatives and limiting members of the class are Wald's test and the locally most powerful test. It is demonstrated that the locally most powerful test has the highest and Wald's test has the lowest asymptotic power when an asymptotically unbalanced sequence of ANOVA designs is considered under Pitman…

条件对数线性模型检验的功效函数AI 解读

In fitting a log-linear model to data, it is common to examine the P values associated with the conditional likelihood-ratio tests corresponding to a nested sequence of candidate log-linear models. For an appropriate Pitman sequence of models these test statistics are asymptotically independent and chi-squared in distribution. This article is an analytic study of the noncentrality parameters of these limiting distributions, pointing out factors that determine the powers of…

任意底层分布下方差分量估计的比较AI 解读

Large-sample covariance matrices for the analysis of variance (ANOVA), minimum norm quadratic unbiased estimator (MINQUE), restricted maximum likelihood (REML), and maximum likelihood (ML) estimates of variance components are presented for the unbalanced one-way model when the underlying distributions are not necessarily normal. The limiting variances depend on the design sequence, on the actual values of the variance components, and on the kurtosis parameters of the…

可计算的 MINQUE 型方差分量估计AI 解读

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…

可计算的 MINQUE 型方差分量估计AI 解读

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…

非正态不平衡嵌套混合模型中方差分量 ANOVA 估计的渐近正态性AI 解读

Despite their lack of optimality in unbalanced normally distributed models, the ANOVA estimates of components of variance are convenient and widely used. The hierarchal (nested) design is well suited to this estimation scheme. In this paper the nonnormal, unbalanced hierarchal design is considered and mild conditions for a sequence of such designs are specified so that the vector of normalized ANOVA estimates converges to a multivariate normal distribution. The nested…