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, whether considered pairwise or collectively.

翻译：本文针对双向交叉混合效应模型中极大似然估计和约束极大似然估计（REML）的渐近性质展开研究，探讨当行数、列数及单元格数趋于无穷大时的统计行为。在无需正态性假设的极弱条件下，证明了这些估计量具有渐近正态性，且其协方差矩阵呈现结构化特征。对于行数、列数及单元格数的增长速率，无论成对考虑还是整体考虑，均无任何限制条件。