Set estimation under convexity type assumptions

By A. Casal. 2007

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On Statistical Properties of Sets Fulfilling Rolling-Type Conditions (2011, background): “Rodŕıguez-Casal [29] studied its properties as an estimator of S and ∂S, providing (under some rolling-type assumptions for S) convergence rates for dH(Sn, S), dH(∂Sn, ∂S) and dμ(Sn, S) which essentially coincide with those given by Dümbgen and Walther [12] for the convex case.”
Set estimation: another bridge between statistics and geometry (2009, methodology): “A recent example is the work by Cuevas, Fraiman and Rodríguez-Casal (2007) on the estimation of the measure of the boundary of S, as de ned by the so-called Minkowski content.”