Uniform Laws of Large Numbers for Empirical Associated Functionals of Random Closed Sets
Ilya S. Molchanov · Theory of Probability and Its Applications · 1988
Previous article Next article Uniform Laws of Large Numbers for Empirical Associated Functionals of Random Closed SetsI. S. MolchanovI. S. Molchanovhttps://doi.org/10.1137/1132086PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. Matheron, Random sets and integral geometry, John Wiley & Sons, New York-London-Sydney, 1975xxiii+261 52:6828 0321.60009 Google Scholar[2] I. S. Molchanov, A generalization of the Choquet theorem for random sets with a given class of realizations, Theory of Probability and Mathematical Statistics, 28 (1984), 99–106 0541.60010 Google Scholar[3] R. N. Bhattacharya and , R. Ranga Rao, Normal approximation and asymptotic expansions, John Wiley & Sons, New York-London-Sydney, 1976xiv+274 55:9219 0331.41023 Google Scholar[4] Flemming Topsøe, On the Glivenko-Cantelli theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 14 (1969/70), 239–250 45:1230 0185.46701 CrossrefGoogle Scholar[5] J. Serra, Image analysis and mathematical morphology, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1984xviii+610 87d:68106 0565.92001 Google Scholar[6] P. S. Aleksandrov, Introduction to Set Theory and General Topology, Nauka, Moscow, 1977, (In Russian.) Google Scholar[7] I. S. Molchanov, The Glivenko–Cantelli theorem for random closed sets, Fourth International Vilnius Conference on Probability Theory and Mathematical Statistics, Vol. 2, Lith. Acad. Sci. Inst. Math. and Cybern., 1985, 211–212, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Random Closed Sets and Capacity Functionals10 November 2017 Cross Ref Expectations of Random Sets10 November 2017 Cross Ref Minkowski Sums10 November 2017 Cross Ref Unions of Random Sets10 November 2017 Cross Ref Random Sets and Random Functions10 November 2017 Cross Ref References7 April 2015 Cross Ref Level sets estimation and Vorob’ev expectation of random compact setsSpatial Statistics, Vol. 2 Cross Ref A Limit theorem for scaled vacancies of the boolean model4 April 2007 | Stochastics and Stochastic Reports, Vol. 58, No. 1-2 Cross Ref Statistics of the Boolean model: from the estimation of means to the estimation of distributions1 July 2016 | Advances in Applied Probability, Vol. 27, No. 1 Cross Ref Asymptotic properties of estimators for parameters of the Boolean model1 July 2016 | Advances in Applied Probability, Vol. 26, No. 2 Cross Ref A Consistent Estimate of Parameters of Boolean Models of Random Closed SetsI. S. Molchanov17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 3AbstractPDF (836 KB)Empirical Estimation of Distribution Quantiles of Random Closed SetsI. S. Molchanov17 July 2006 | Theory of Probability & Its Applications, Vol. 35, No. 3AbstractPDF (753 KB)Random Closed Sets Cross Ref Volume 32, Issue 3| 1988Theory of Probability & Its Applications History Submitted:12 June 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1132086Article page range:pp. 556-559ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics