Non-finite Fisher information and homogeneity: an EM approach

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Testing the Number of Components in Normal Mixture Regression Models (2015, methodology): “We propose a modified EM test by building on this local quadratic representation and extending the EM approach pioneered by Li, Chen, and Marriott (2009) and Li and Chen (2010).”
Testing the Order of a Finite Mixture (2010, methodology): “To develop a method without such restrictive conditions on the mixture models, Li, Chen, and Marriott (2009) and Chen and Li (2009) have proposed an EM test.”
Finite mixture models and model-based clustering (2010, background): “Another possibility includes defining a penalized log likelihood function [28, 67] that contains a penalty term preventing the log likelihood from going to infinity by construction.”
Singularity, misspecification and the convergence rate of EM (2018, background): “This problem is known to be challenging due to the break-down of the (generalized) likelihood ratio test around the singularity of the Fisher information matrix; see the papers [19, 5] for some past work on the problem.”