A Consistent Estimate of Parameters of Boolean Models of Random Closed Sets
Ilya S. Molchanov · Theory of Probability and Its Applications · 1992
Previous article Next article A Consistent Estimate of Parameters of Boolean Models of Random Closed SetsI. S. MolchanovI. S. Molchanovhttps://doi.org/10.1137/1136073PDFBibTexSections 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, Uniform laws of large numbers for empirical associated functionals of random closed sets, Theory Probab. Appl., 32 (1987), 556–559 10.1137/1132086 0644.60028 LinkGoogle Scholar[3] D. Stoyan, , W. S. Kendall and , J. Mecke, Stochastic geometry and its applications, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons Ltd., Chichester, 1987, 345– 88j:60034a 0622.60019 Google Scholar[4] R. V. Ambartsumyan, , J. Mecke and , D. Stoyan, Introduction in Stochastic Geometry, Nauka, Moscow, , (In Russian.) Google Scholar[5] I. S. Molchanov, On convergence of empirical accompanying functionals of stationary random sets, Theory Probab. Math. Statist., (1988), 107–109 0664.60018 Google Scholar[6] V. F. Gaposhkin, Criteria for the strong law of large numbers for some classes of second-order stationary processes and homogeneous random fields, Theory Probab. Appl., 22 (1977), 286–313 10.1137/1122034 0377.60033 LinkGoogle Scholar[7] I. S. Molchanov, Masters Thesis, Construction and Estimation of Distributions for Some Classes of Sets, Dissertation, Kiev University, 1986, 139 p. (In Russian.) Google Scholar[8] I. S. Molchanov, Empirical estimation of distribution quantiles of closed random sets, Theory Probab. Appl., 35 (1990), 594–600 10.1137/1135085 0745.62031 LinkGoogle Scholar[9] A. A. Borovkov, Mathematical Statistics, Nauka, Moscow, 1984, (In Russian.) Google Scholar[10] J.-P. Serra, Image Analysis and Mathematical Morphology, Academic Press, London, 1982 0565.92001 Google Scholar[11] Kurt Leichtweiss, Konvexe Mengen, Springer-Verlag, Berlin, 1980330 pp. (loose errata) 81j:52001 0427.52001 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Generalization of Portmanteau Theorem with Respect to the Pseudoweak Convergence of Random Closed SetsT. Grbić and E. PapTheory of Probability & Its Applications, Vol. 54, No. 1 | 17 February 2012AbstractPDF (223 KB)The stochastic geometry of polymer crystallization processes 1Stochastic Analysis and Applications, Vol. 15, No. 3 | 1 Jan 1997 Cross Ref Set-Valued Estimators for Mean Bodies Related to Boolean ModelsStatistics, Vol. 28, No. 1 | 5 July 2007 Cross Ref Directional analysis of fibre processes related to Boolean modelsMetrika, Vol. 41, No. 1 | 1 Dec 1994 Cross Ref Volume 36, Issue 3| 1992Theory of Probability & Its Applications427-645 History Submitted:13 February 1989Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136073Article page range:pp. 600-607ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics