# Increasing dimension asymptotics for two-way crossed mixed effect models

arXiv: https://arxiv.org/abs/2401.06446 · HTML: https://mlsanity.com/paper/2401.06446/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2024.

## Built on by (most cited first, 1 of 1)

- [Gradient Boosted Mixed Models: Flexible Estimation of Mean and Variance Components for Clustered Data](https://mlsanity.com/paper/2511.00217/) (2025)

## Abstract (arXiv)

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.