Increasing Dimension Asymptotics for Two-way Crossed Mixed Effect Model

Abstract

This presentation discusses the asymptotic behaviors of maximum likelihood and restricted maximum likelihood (REML) estimators within a two-way crossed mixed effect model, where the numbers of rows, columns, and cells increase indefinitely. It demonstrates that these estimators achieve asymptotic normality under very mild conditions that do not require normal distribution assumptions, and they exhibit a well-structured covariance matrix. The expansion rate of rows, columns, and cells is flexible, with no restrictions on their individual or combined growth. Additionally, we establish the asymptotic normal distribution for empirical best linear unbiased predictions (EBLUPs) and subsequently derive prediction intervals for these EBLUPs.