This analysis reveals real positive critical points of the likelihood function in squared linear models, indicating their robust structure.
We study statistical models that are parametrized by squares of linear forms. All critical points of the likelihood function are real and positive. There is one for each region of the projective hyperplane arrangement. We study the ideal and singular locus of the model, and we give a determinantal presentation for its likelihood correspondence. We characterize tropical degenerations of the MLE, and we describe log-normal polytopes.
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Friedman et al. (2025) studied this question.
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