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Abstract
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We study logarithmic Voronoi cells for linear statistical models and partial linear
models. The logarithmic Voronoi cells at points on such model are polytopes. To any
-dimensional linear model
inside the probability simplex
,
we can associate an
matrix
.
For interior points, we describe the vertices of these polytopes in terms of cocircuits of
. We also show
that these polytopes are combinatorially isomorphic to the dual of a vector configuration with
Gale diagram
.
This means that logarithmic Voronoi cells at all interior points on a linear model
have the same combinatorial type. We also describe logarithmic Voronoi cells at
points on the boundary of the simplex. Finally, we study logarithmic Voronoi cells of
partial linear models, where the points on the boundary of the model are
especially of interest.
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Keywords
maximum likelihood estimation, linear models, polytopes,
logarithmic Voronoi cells, Gale diagrams, boundary, partial
linear models, combinatorial type, statistics, probability
simplex
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Mathematical Subject Classification
Primary: 51M20, 52A40, 62F10
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Milestones
Received: 14 December 2022
Revised: 10 June 2023
Accepted: 3 July 2023
Published: 11 January 2024
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© 2024 MSP (Mathematical Sciences
Publishers). |
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