On the maximum likelihood degree of linear mixed models with two variance components

2016/08/31 by Mariusz Grządziel, Grzadziel, Mariusz
Mathematics · Decision Sciences · #Statistical Methods and Inference #Markov Chains and Monte Carlo Methods #Optimal Experimental Design Methods

paper · pdf · doi:10.48550/arxiv.1608.08789

Abstract

We extend the results concerning the upper bounds for the maximum likelihood degree and the REML degree of the one-way random effects model presented in Gross et al. [Electron. J. Stat. 6 (2012), pp. 993-1016] to the case of the normal linear mixed model with two variance components. Then we prove that both parts of Conjecture 1 in the paper of Gross et al., which concerns a certain extension of the one-way random effects model, are true under fairly mild conditions.

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