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. 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

Figures from this paper

Optimality of Maximum Likelihood for Log-Concave Density Estimation and Bounded Convex Regression
High-dimensional nonparametric density estimation via symmetry and shape constraints
The Log-Concave Maximum Likelihood Estimator is Optimal in High Dimensions
A new computational framework for log-concave density estimation
On the Minimal Error of Empirical Risk Minimization

References

SHOWING 1-10 OF 69 REFERENCES
Adaptation in log-concave density estimation
Global rates of convergence in log-concave density estimation
NONPARAMETRIC ESTIMATION OF MULTIVARIATE CONVEX-TRANSFORMED DENSITIES.
...
1
2
3
4
5
...