APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA RÉNYI DIVERGENCES.

@article{Han2016APPROXIMATIONAE,
  title={APPROXIMATION AND ESTIMATION OF s-CONCAVE DENSITIES VIA R{\'E}NYI DIVERGENCES.},
  author={Qiyang Han and J. Wellner},
  journal={Annals of statistics},
  year={2016},
  volume={44 3},
  pages={
          1332-1359
        }
}
In this paper, we study the approximation and estimation of s-concave densities via Rényi divergence. We first show that the approximation of a probability measure Q by an s-concave density exists and is unique via the procedure of minimizing a divergence functional proposed by [Ann. Statist.38 (2010) 2998-3027] if and only if Q admits full-dimensional support and a first moment. We also show continuity of the divergence functional in Q: if Qn → Q in the Wasserstein metric, then the projected… Expand
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