메뉴 건너뛰기




Volumn 141, Issue 3-4, 2008, Pages 333-387

Uniform central limit theorems for kernel density estimators

Author keywords

Kernel density estimation; Plug in property; Smoothed empirical processes; Uniform central limit theorem

Indexed keywords


EID: 42149093784     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0087-9     Document Type: Article
Times cited : (59)

References (33)
  • 1
    • 0001240707 scopus 로고
    • Central limit theorems for stochastic processes under random entropy conditions
    • Alexander K.S. (1987). Central limit theorems for stochastic processes under random entropy conditions. Probab. Theory Relat. Fields 75: 351-378
    • (1987) Probab. Theory Relat. Fields , vol.75 , pp. 351-378
    • Alexander, K.S.1
  • 3
    • 0041857920 scopus 로고    scopus 로고
    • Nonparametric estimators which can be 'plugged-in'
    • Bickel J.P. and Ritov Y. (2003). Nonparametric estimators which can be 'plugged-in'. Ann. Statist. 31: 1033-1053
    • (2003) Ann. Statist. , vol.31 , pp. 1033-1053
    • Bickel, J.P.1    Ritov, Y.2
  • 6
    • 0002485879 scopus 로고
    • Sample functions of the Gaussian process
    • Dudley R.M. (1973). Sample functions of the Gaussian process. Ann. Probab. 1: 66-103
    • (1973) Ann. Probab. , vol.1 , pp. 66-103
    • Dudley, R.M.1
  • 7
    • 0001151383 scopus 로고
    • An extended Wichura theorem, definition of Donsker class, and weighted empirical distributions
    • Springer, New York
    • Dudley, R.M.: An extended Wichura theorem, definition of Donsker class, and weighted empirical distributions. Lecture Notes in Mathematics, vol. 1153, pp. 141-178. Springer, New York (1985)
    • (1985) Lecture Notes in Mathematics , vol.1153 , pp. 141-178
    • Dudley, R.M.1
  • 10
    • 33746227538 scopus 로고    scopus 로고
    • Concentration inequalities and asymptotic results for ratio type empirical processes
    • Giné E. and Koltchinskii V. (2006). Concentration inequalities and asymptotic results for ratio type empirical processes. Ann. Probab. 34: 1143-1216
    • (2006) Ann. Probab. , vol.34 , pp. 1143-1216
    • Giné, E.1    Koltchinskii, V.2
  • 11
    • 0000145024 scopus 로고
    • Some limit theorems for empirical processes
    • Giné E. and Zinn J. (1984). Some limit theorems for empirical processes. Ann. Probab. 12: 929-989
    • (1984) Ann. Probab. , vol.12 , pp. 929-989
    • Giné, E.1    Zinn, J.2
  • 12
    • 0001678367 scopus 로고
    • Empirical processes indexed by Lipschitz functions
    • Giné E. and Zinn J. (1986). Empirical processes indexed by Lipschitz functions. Ann. Probab. 14: 1329-1338
    • (1986) Ann. Probab. , vol.14 , pp. 1329-1338
    • Giné, E.1    Zinn, J.2
  • 13
    • 0012799913 scopus 로고
    • Gaussian characterization of uniform Donsker classes
    • Giné E. and Zinn J. (1991). Gaussian characterization of uniform Donsker classes. Ann. Probab. 19: 758-782
    • (1991) Ann. Probab. , vol.19 , pp. 758-782
    • Giné, E.1    Zinn, J.2
  • 16
    • 34249095345 scopus 로고
    • Relationships between Donsker classes and Sobolev spaces
    • Marcus D.J. (1985). Relationships between Donsker classes and Sobolev spaces. Z. Wahrsch. Verw. Gebiete 69: 323-330
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.69 , pp. 323-330
    • Marcus, D.J.1
  • 17
    • 34248996136 scopus 로고    scopus 로고
    • Empirical and Gaussian processes on Besov classes
    • Giné, E., Koltchinskii, V., Li, W., Zinn, J. (eds.) High dimensional probability IV
    • Nickl, R.: Empirical and Gaussian processes on Besov classes. In: Giné, E., Koltchinskii, V., Li, W., Zinn, J. (eds.): High dimensional probability IV, IMS Lecture Notes, vol. 51, pp. 185-195 (2006a)
    • (2006) IMS Lecture Notes , vol.51 , pp. 185-195
    • Nickl, R.1
  • 19
    • 34248222659 scopus 로고    scopus 로고
    • Donsker-type theorems for nonparametric maximum likelihood estimators
    • Nickl R. (2007). Donsker-type theorems for nonparametric maximum likelihood estimators. Probab. Theory Relat. Fields 138: 411-449
    • (2007) Probab. Theory Relat. Fields , vol.138 , pp. 411-449
    • Nickl, R.1
  • 20
    • 34249036798 scopus 로고    scopus 로고
    • Bracketing metric entropy rates and empirical central limit theorems for function classes of Besov- and Sobolev-type
    • Nickl R. and Pötscher B.M. (2007). Bracketing metric entropy rates and empirical central limit theorems for function classes of Besov- and Sobolev-type. J. Theoret. Probab. 20: 177-199
    • (2007) J. Theoret. Probab. , vol.20 , pp. 177-199
    • Nickl, R.1    Pötscher, B.M.2
  • 28
    • 0001742955 scopus 로고
    • Weak convergence of smoothed empirical processes
    • Vaart A.W. (1994). Weak convergence of smoothed empirical processes. Scand. J. Statist. 21: 501-504
    • (1994) Scand. J. Statist. , vol.21 , pp. 501-504
    • Van Der Vaart, A.W.1
  • 31
    • 0001581756 scopus 로고
    • Weak convergence of smoothed empirical processes
    • Yukich J.E. (1992). Weak convergence of smoothed empirical processes. Scand. J. Statist. 19: 271-279
    • (1992) Scand. J. Statist. , vol.19 , pp. 271-279
    • Yukich, J.E.1
  • 32
    • 0031211854 scopus 로고    scopus 로고
    • Functional central limit theorems for triangular arrays of function-indexed processes under uniformly integrable entropy conditions
    • Ziegler K. (1997). Functional central limit theorems for triangular arrays of function-indexed processes under uniformly integrable entropy conditions. J. Multivar. Anal. 62: 233-272
    • (1997) J. Multivar. Anal. , vol.62 , pp. 233-272
    • Ziegler, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.