Precise Linear Mixed Model Asymptotics: the Crossed Case

Abstract

Precise asymptotics for linear mixed models is a topic that the speaker became involved with, against the grain of his other research, in the late 2010s. It has since led to papers in Biometrika and Journal of the Royal Statistics Society, Series B for the nested case. This talk will focus on the more challenging crossed case, which enjoyed good progress during the speaker's 2024 sabbatical. In addition to the usual selling points of approximate inference, optimal design and sample size calculations, a new pay-off will be discussed: estimator behaviour. In particular, intriguing similarities between maximum likelihood estimators for linear mixed models with nested and crossed random effects will be exposed. This research has involved collaborations with Aishwarya Bhaskaran, Swarnadip Ghosh, Jiming Jiang and Luca Maestrini.