Corpus ID: 88522363

Multivariate convex regression: global risk bounds and adaptation

@article{Han2016MultivariateCR,
  title={Multivariate convex regression: global risk bounds and adaptation},
  author={Qiyang Han and J. Wellner},
  journal={arXiv: Statistics Theory},
  year={2016}
}
We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the multivariate setting $(d\geq 2)$. One crucial fact is that the minimax risks depend heavily on the shape of the support of the regression function. It is shown that the global minimax risk is on the order of $n^{-2/(d+1)}$ when the support is sufficiently smooth… Expand

Figures from this paper

Optimality of Maximum Likelihood for Log-Concave Density Estimation and Bounded Convex Regression
Adaptation in log-concave density estimation
Max-affine regression with universal parameter estimation for small-ball designs
...
1
2
3
4
...

References

SHOWING 1-10 OF 62 REFERENCES
Global risk bounds and adaptation in univariate convex regression
Model selection for regression on a random design
A new perspective on least squares under convex constraint
Entropy of Convex Functions on ℝ d.
Consistency of Multidimensional Convex Regression
Risk bounds for model selection via penalization
...
1
2
3
4
5
...