Squared Linear Models
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909858212610048 |
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| author | Friedman, Hannah Sturmfels, Bernd Wiesmann, Maximilian |
| author_facet | Friedman, Hannah Sturmfels, Bernd Wiesmann, Maximilian |
| contents | 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 critical point in each region of the projective hyperplane arrangement defined by the linear forms. We examine 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, we describe the log-normal polytopes, and we explore connections to determinantal point processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Squared Linear Models Friedman, Hannah Sturmfels, Bernd Wiesmann, Maximilian Commutative Algebra Algebraic Geometry Statistics Theory 13P25, 62R01, 14Q30 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 critical point in each region of the projective hyperplane arrangement defined by the linear forms. We examine 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, we describe the log-normal polytopes, and we explore connections to determinantal point processes. |
| title | Squared Linear Models |
| topic | Commutative Algebra Algebraic Geometry Statistics Theory 13P25, 62R01, 14Q30 |
| url | https://arxiv.org/abs/2505.19351 |