WITHDRAWN Increasing Dimension Asymptotics for Two-Way Crossed Mixed Effect Model

This presentation talks about 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.

Crossed random effect

Maximum likelihood estimator

Kronecker product

Variance components

Asymptotic independence