# 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 Jon A. 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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