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2017

Geometry of Log-Concave Density Estimation

Robeva, Elina, Sturmfels, Bernd, Uhler, Caroline

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Shape-constrained density estimation is an important topic in mathematical statistics.

We focus on densities on $\mathbb{R}^d$ that are log-concave, and we study geometric properties of the maximum likelihood estimator (MLE) for weighted samples.
Cule, Samworth, and Stewart showed that the logarithm of the optimal log-concave density is piecewise linear and supported on a regular subdivision of the samples.
This defines a map from the space of weights to the set of regular subdivisions of the samples, i.e.

Geometry of Log-Concave Density Estimation · Around

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