Adaptation in multivariate log-concave density estimation

@article{Feng2020AdaptationIM,
  title={Adaptation in multivariate log-concave density estimation},
  author={Oliver Y. Feng and Adityanand Guntuboyina and Arlene K. H. Kim and R. J. Samworth},
  journal={arXiv: Statistics Theory},
  year={2020}
}
We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over two subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine. The complexity of such densities $f$ can be measured in terms of the sum $\Gamma(f)$ of the numbers of facets of the subdomains in the polyhedral subdivision of the support induced by $f$. Given $n$ independent observations from a $d$-dimensional log-concave… Expand
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