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Original Articles

Surface area estimation under convexity type assumptions

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Pages 729-741 | Received 23 Oct 2008, Published online: 22 Jul 2009

References

  • Cuevas , A. , Fraiman , R. and Rodríguez-Casal , A. 2007 . A nonparametric approach to the estimation of lengths and surface areas . Ann. Statist. , 35 ( 3 ) : 1031 – 1051 .
  • Dümbgen , L. and Walther , G. 1996 . Rates of convergence for random approximations of convex sets . Adv. Appl. Probab. , 28 ( 2 ) : 384 – 393 .
  • Bräker , H. and Hsing , T. 1998 . On the area and perimeter of a random convex hull in a bounded convex set . Probab. Theory Related Fields , 111 ( 4 ) : 517 – 550 .
  • Rodríguez-Casal , A. 2007 . Set estimation under convexity type assumptions . Ann. l'I.H.P.- Probab. Statist. , 43 : 763 – 774 .
  • Mattila , P. 1995 . Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability , Cambridge : Cambridge University Press .
  • Pateiro-López , B. and Rodríguez-Casal , A. 2008 . Length and surface area estimation under smoothness restrictions . Adv. Appl. Probab. , 40 ( 2 ) : 348 – 358 .
  • Walther , G. 1999 . On a generalization of Blaschke's rolling theorem and the smoothing of surfaces . Math. Methods Appl. Sci. , 22 ( 4 ) : 301 – 316 .
  • Federer , H. 1959 . Curvature measures . Trans. Amer. Math. Soc. , 93 : 418 – 491 .
  • Pateiro-López , B. 2008 . “ Set estimation under convexity type restrictions ” . Universidade de Santiago de Compostela . Ph.D. Diss

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