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In this paper, we study the approximation and estimation of sconcave densities via Rényi divergenceWe first show that the approximation of a probability measure Q by an sconcave density exists and is unique via the procedure of minimizing a divergence functional proposed by Ann Statist 38 (10) 2998–3027 if and only if Q admits fulldimensional support and a first424 G GRIPENBERG (ii) the function s i> h(s)d=g(s)/s is nonincreasing on (0,oo) Then the trivial solution x(t) = 0 of the equation Jo is unique if and only ifT ² x t t g x t When t 0 this equation is just an identity When t 1 it gives 30 from ECONOMICS 1404 at Massachusetts Institute of Technology
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