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非平衡交叉设计中协方差矩阵的逆AI 解读

SUMMARY This paper addresses a long-standing open problem in crossed random-effects models under unbalanced designs: how to find an analytic expression for the inverse of $ {V} $, the covariance matrix of the observed response. For unbalanced crossed designs, $ {V} $ is dense, and the lack of a closed-form representation for $ {V}^{-1} $ has, until now, made the use of likelihood-based methods computationally challenging and difficult to analyse mathematically. We use the…

双向交叉混合效应模型的维度增长渐近理论AI 解读

This paper presents asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model as the sizes of the rows, columns, and cells tend to infinity. Under very mild conditions which do not require the assumption of normality, the estimators are proven to be asymptotically normal, possessing a structured covariance matrix. The growth rate for the number of rows, columns, and cells is unrestricted,…

嵌套误差回归模型中经验最佳线性无偏预测的渐近理论AI 解读

In this article we derive the asymptotic distribution of estimated best linear unbiased predictors (EBLUPs) of the random effects in a nested error regression model. Under very mild conditions which do not require the assumption of normality, we show that asymptotically the distribution of the EBLUPs as both the number of clusters and the cluster sizes diverge to infinity is the convolution of the true distribution of the random effects and a normal distribution. This result…