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，在行数、列数及单元数趋于无穷大时，给出了最大似然估计和约束最大似然估计的渐近结果。在不需要正态性假设的非常温和条件下，证明了这些估计量具有渐近正态性，且协方差矩阵具有结构特征。行数、列数及单元数的增长率不受任何限制，无论成对考虑还是集体考虑均成立。