메뉴 건너뛰기




Volumn 44, Issue 2, 2012, Pages 311-329

On statistical properties of sets fulfilling rolling-type conditions

Author keywords

Boundary length; Excess mass; Glivenko Cantelli class; Positive reach; R convexity; Rolling condition; Set estimation

Indexed keywords

BOUNDARY LENGTH; EXCESS MASS; GLIVENKO-CANTELLI CLASS; POSITIVE REACH; R-CONVEXITY; ROLLING CONDITIONS;

EID: 84872074050     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1339878713     Document Type: Article
Times cited : (74)

References (32)
  • 1
    • 52949118810 scopus 로고    scopus 로고
    • Outer Minkowski content for some classes of closed sets
    • Ambrosio, L., Colesanti, A. and Villa, E. (2008). Outer Minkowski content for some classes of closed sets. Math. Ann. 342, 727-748.
    • (2008) Math. Ann. , vol.342 , pp. 727-748
    • Ambrosio, L.1    Colesanti, A.2    Villa, E.3
  • 2
    • 0035710509 scopus 로고    scopus 로고
    • On the estimation of a star-shaped set
    • Baíllo, A. and Cuevas, A. (2001). On the estimation of a star-shaped set. Adv. Appl. Prob. 33, 717-726.
    • (2001) Adv. Appl. Prob. , vol.33 , pp. 717-726
    • Baíllo, A.1    Cuevas, A.2
  • 3
    • 54049083901 scopus 로고    scopus 로고
    • Exact rates in density support estimation
    • Biau, G., Cadre, B. and Pelletier, B. (2008). Exact rates in density support estimation. J. Multivariate Anal. 99, 2185-2207.
    • (2008) J. Multivariate Anal. , vol.99 , pp. 2185-2207
    • Biau, G.1    Cadre, B.2    Pelletier, B.3
  • 4
    • 77956109927 scopus 로고    scopus 로고
    • Asymptotic normality in density support estimation
    • Biau, G., Cadre, B., Mason, D. M. and Pelletier, B. (2009). Asymptotic normality in density support estimation. Electron. J. Prob. 14, 2617-2635.
    • (2009) Electron. J. Prob. , vol.14 , pp. 2617-2635
    • Biau, G.1    Cadre, B.2    Mason, D.M.3    Pelletier, B.4
  • 6
    • 0043115373 scopus 로고
    • Uniform convergence of probability measures on classes of functions
    • Bickel, P. J. and Millar, P.W. (1992). Uniform convergence of probability measures on classes of functions. Statist. Sinica 2, 1-15.
    • (1992) Statist. Sinica , vol.2 , pp. 1-15
    • Bickel, P.J.1    Millar, P.W.2
  • 8
    • 84920043699 scopus 로고    scopus 로고
    • Set estimation
    • eds W. S. Kendall and I. Molchanov, Oxford University Press
    • Cuevas, A. and Fraiman, R. (2009). Set estimation. In New Perspectives on Stochastic Geometry, eds W. S. Kendall and I. Molchanov, Oxford University Press, pp. 366-389.
    • (2009) New Perspectives on Stochastic Geometry , pp. 366-389
    • Cuevas, A.1    Fraiman, R.2
  • 10
    • 49349094933 scopus 로고    scopus 로고
    • A nonparametric approach to the estimation of lengths and surface areas
    • Cuevas, A., Fraiman, R. and Rodríguez-Casal, A. (2007). A nonparametric approach to the estimation of lengths and surface areas. Ann. Statist. 35, 1031-1051.
    • (2007) Ann. Statist. , vol.35 , pp. 1031-1051
    • Cuevas, A.1    Fraiman, R.2    Rodríguez-Casal, A.3
  • 12
    • 0008364462 scopus 로고    scopus 로고
    • Rates of convergence for random approximations of convex sets
    • Dümbgen, L. andWalther, G. (1996). Rates of convergence for random approximations of convex sets. Adv. Appl. Prob. 28, 384-393.
    • (1996) Adv. Appl. Prob. , vol.28 , pp. 384-393
    • L, D.N.A.D.1    Walther, G.2
  • 15
    • 0001341972 scopus 로고
    • Estimation of a convex density contour in two dimensions
    • Hartigan, J. A. (1987). Estimation of a convex density contour in two dimensions. J. Amer. Statist. Assoc. 82, 267-270.
    • (1987) J. Amer. Statist. Assoc. , vol.82 , pp. 267-270
    • Hartigan, J.A.1
  • 16
    • 79551602277 scopus 로고    scopus 로고
    • Nonparametric estimation of surface integrals
    • Jiménez, R. and Yukich, J. E. (2011). Nonparametric estimation of surface integrals. Ann. Statist. 39, 232-260.
    • (2011) Ann. Statist. , vol.39 , pp. 232-260
    • Jiménez, R.1    Yukich, J.E.2
  • 17
    • 0041082260 scopus 로고
    • Characterizations of convex sets
    • eds P. M. Gruber and J. M.Wills North-Holland, Amsterdam
    • Mani-Levitska, P. (1993) Characterizations of convex sets. In Handbook of Convex Geometry, eds P. M. Gruber and J. M.Wills, North-Holland, Amsterdam, pp. 19-41.
    • (1993) Handbook of Convex Geometry , pp. 19-41
    • Mani-Levitska, P.1
  • 18
    • 69149089372 scopus 로고    scopus 로고
    • Asymptotic normality of plug-in level set estimates
    • Mason, D. M. and Polonik, W. (2009). Asymptotic normality of plug-in level set estimates. Ann. Appl. Prob. 19, 1108-1142.
    • (2009) Ann. Appl. Prob. , vol.19 , pp. 1108-1142
    • Mason, D.M.1    Polonik, W.2
  • 20
    • 0000371878 scopus 로고
    • Excess mass estimates and tests for multimodality
    • Müller, D. W. and Sawitzki, G. (1991). Excess mass estimates and tests for multimodality. J. Amer. Statist. Assoc. 86, 738-746.
    • (1991) J. Amer. Statist. Assoc. , vol.86 , pp. 738-746
    • Müller, D.W.1    Sawitzki, G.2
  • 21
    • 49349086609 scopus 로고    scopus 로고
    • Length and surface area estimation under smoothness restrictions
    • Pateiro-López, B. and Rodríguez-Casal, A. (2008). Length and surface area estimation under smoothness restrictions. Adv. Appl. Prob. 40, 348-358.
    • (2008) Adv. Appl. Prob. , vol.40 , pp. 348-358
    • Pateiro-López, B.1    Rodríguez-Casal, A.2
  • 22
    • 77953201888 scopus 로고    scopus 로고
    • Generalizing the convex hull of a sample: The R package alphahull
    • Pateiro-López, B. and Rodríguez-Casal, A. (2010). Generalizing the convex hull of a sample: the R package alphahull. J. Statist. Software 34, 1-28.
    • (2010) J. Statist. Software , vol.34 , pp. 1-28
    • Pateiro-López, B.1    Rodríguez-Casal, A.2
  • 23
    • 0039303073 scopus 로고
    • Sur les ensembles ε-convexes
    • Perkal, J. (1956). Sur les ensembles ε-convexes. Colloq. Math. 4, 1-10.
    • (1956) Colloq. Math. , vol.4 , pp. 1-10
    • Perkal, J.1
  • 25
    • 0001030653 scopus 로고
    • Measuring mass concentrations and estimating density contour clusters-an excess mass approach
    • Polonik, W. (1995). Measuring mass concentrations and estimating density contour clusters - an excess mass approach. Ann. Statist. 23, 855-881.
    • (1995) Ann. Statist. , vol.23 , pp. 855-881
    • Polonik, W.1
  • 26
    • 18644381620 scopus 로고    scopus 로고
    • Estimation of regression contour clusters - An application of the excess mass approach to regression
    • Polonik, W. and Wang, Z. (2005). Estimation of regression contour clusters - an application of the excess mass approach to regression. J. Multivariate Anal. 94, 227-249.
    • (2005) J. Multivariate Anal. , vol.94 , pp. 227-249
    • Polonik, W.1    Wang, Z.2
  • 27
    • 30644468967 scopus 로고    scopus 로고
    • On boundaries of unions of sets with positive reach
    • Rataj, J. (2005). On boundaries of unions of sets with positive reach. Beiträge Algebra Geom. 46, 397-404.
    • (2005) Beiträge Algebra Geom. , vol.46 , pp. 397-404
    • Rataj, J.1
  • 28
    • 84920034477 scopus 로고    scopus 로고
    • Random polytopes
    • edsW. S. Kendall and I. Molchanov, Oxford University Press
    • Reitzner, M. (2009). Random polytopes. In New Perspectives on Stochastic Geometry, edsW. S. Kendall and I. Molchanov, Oxford University Press, pp. 45-75.
    • (2009) New Perspectives on Stochastic Geometry , pp. 45-75
    • Reitzner, M.1
  • 31
    • 0031316270 scopus 로고    scopus 로고
    • Granulometric smoothing
    • Walther, G. (1997). Granulometric smoothing. Ann. Statist. 25, 2273-2299.
    • (1997) Ann. Statist. , vol.25 , pp. 2273-2299
    • Walther, G.1
  • 32
    • 0346615742 scopus 로고    scopus 로고
    • On a generalization of Blaschke's rolling theorem and the smoothing
    • Walther, G. (1999). On a generalization of Blaschke's rolling theorem and the smoothing. Math. Methods Appl. Sci. 22, 301-316.
    • (1999) Math. Methods Appl. Sci. , vol.22 , pp. 301-316
    • Walther, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.