Rates of convergence for random approximations of convex sets

Advances in Applied Probability

Volumn 28, Issue 2, 1996, Pages 384-393

  Dümbgen, Lutz ^a   Walther, Günther ^b  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Convex set; Duality; Packing numbers; Polar set; Probability inequality; Rate of convergence

Indexed keywords

EID: 0008364462     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800048539     Document Type: Article

References (8)

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2. BURAGO, Y. D. AND ZALGALLER, V. A. (1988) Geometric Inequalities. Springer, New York.
3. FEDERER, H. (1969) Geometric Measure Theory. Springer, Berlin.
4. POLLARD, D. (1990) Empirical Processes: Theory and Applications. (NSF-CBMS Regional Conf. Series Prob. Statist. 2) IMS, Hayward, CA.
5. SCHNEIDER, R. (1988) Random approximation of convex sets. J. Microsc. 151, 211-227.
6. SCHNEIDER, R. (1993) Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press, Cambridge.
7. SMALL, C. G. (1991) Reconstructing convex bodies from random projected images. Canadian J. Statist. 19, 341-347.
8. WEIL, W. AND WIEACKER, J. A. (1993) Stochastic Geometry. In Handbook of Convex Geometry, Vol. B. ed. P. M. Gruber and J. M. Wills. pp. 1391-1438. Elsevier, Amsterdam.