메뉴 건너뛰기




Volumn 61, Issue 3, 2003, Pages 321-336

Necessary and sufficient conditions for weak convergence of smoothed empirical processes

Author keywords

Bracketing numbers; Empirical processes; Hellinger differentiability; Histogram estimators; Metric entropy; Weak convergence

Indexed keywords


EID: 0037307503     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(02)00395-4     Document Type: Article
Times cited : (7)

References (18)
  • 1
    • 0003456378 scopus 로고
    • The Central Limit Theorem for Real and Banach Valued Random Variables
    • Wiley, New York
    • Araujo, A., Giné, E., 1980. The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York.
    • (1980)
    • Araujo, A.1    Giné, E.2
  • 2
    • 0001666999 scopus 로고
    • Limit theorems for U-processes
    • Arcones, M., Giné, E., 1993. Limit theorems for U-processes. Ann. probab. 21 (3), 1494-1542.
    • (1993) Ann. Probab. , vol.21 , Issue.3 , pp. 1494-1542
    • Arcones, M.1    Giné, E.2
  • 3
    • 0004249893 scopus 로고
    • Probabilistic Techniques in Analysis
    • Springer, Berlin
    • Bass, R., 1995. Probabilistic Techniques in Analysis. Springer, Berlin.
    • (1995)
    • Bass, R.1
  • 4
    • 43949174390 scopus 로고
    • Chung-Smirnov property for perturbed empirical distribution functions
    • Degenhardt, H.J.A., 1993. Chung-Smirnov property for perturbed empirical distribution functions. Statist. Probab. Lett. 16, 97-101.
    • (1993) Statist. Probab. Lett. , vol.16 , pp. 97-101
    • Degenhardt, H.J.A.1
  • 5
    • 0000421687 scopus 로고
    • Central limit theorems for empirical measures
    • (Correction in Vol. 7, pp. 909 - 911)
    • Dudley, R., 1978. Central limit theorems for empirical measures (Correction in Vol. 7, pp. 909 - 911). Ann. probab. 6, 899-929.
    • (1978) Ann. Probab. , vol.6 , pp. 899-929
    • Dudley, R.1
  • 6
    • 0003989054 scopus 로고    scopus 로고
    • Uniform Central Limit Theorems
    • Cambridge University Press, Cambridge
    • Dudley, R., 1999. Uniform Central Limit Theorems. Cambridge University Press, Cambridge.
    • (1999)
    • Dudley, R.1
  • 7
    • 0001227305 scopus 로고
    • The Central Limit Theorem and Epsilon-Entropy
    • Springer, Berlin
    • Dudley, R.M., Strassen, V., 1969. The Central Limit Theorem and Epsilon-Entropy. Lecture Notes in Mathematics. Vol. 87, Springer, Berlin, pp. 224-231.
    • (1969) Lecture Notes in Mathematics , vol.87 , pp. 224-231
    • Dudley, R.M.1    Strassen, V.2
  • 8
    • 4244147272 scopus 로고    scopus 로고
    • On random measure processes with application to smoothed empirical processes
    • Mathematisches Institut, University of Munich, 60, preprint
    • Gaenssler, P., Rost, D., Zieger, K., 1997. On random measure processes with application to smoothed empirical processes. Mathematisches Institut, University of Munich, 60, preprint.
    • (1997)
    • Gaenssler, P.1    Rost, D.2    Zieger, K.3
  • 9
    • 0000145024 scopus 로고
    • Some limit theorems for empirical processes
    • Giné, E., Zinn, J., 1984. Some limit theorems for empirical processes. Ann. Probab. 12, 929-998.
    • (1984) Ann. Probab. , vol.12 , pp. 929-998
    • Giné, E.1    Zinn, J.2
  • 10
    • 0012799913 scopus 로고
    • Gaussian characterization of uniform Donsker classes of functions
    • Giné, E., Zinn, J., 1991. Gaussian characterization of uniform Donsker classes of functions. Ann. Probab. 19, 758-782.
    • (1991) Ann. Probab. , vol.19 , pp. 758-782
    • Giné, E.1    Zinn, J.2
  • 11
    • 0003757756 scopus 로고
    • Asymptotic Methods in Statistical Decision Theory
    • Springer, Berlin
    • LeCam, L., 1986. Asymptotic Methods in Statistical Decision Theory. Springer, Berlin.
    • (1986)
    • LeCam, L.1
  • 12
    • 0003771756 scopus 로고
    • Probability in Banach Spaces: Isoperimetry and Processes
    • Springer, Berlin
    • Ledoux, M., Talagrand, M., 1991. Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin.
    • (1991)
    • Ledoux, M.1    Talagrand, M.2
  • 14
    • 0003983125 scopus 로고
    • Convergence of Stochastic Processes
    • Springer, Berlin
    • Pollard, D., 1984. Convergence of Stochastic Processes. Springer, Berlin.
    • (1984)
    • Pollard, D.1
  • 15
    • 0001024505 scopus 로고
    • On the uniform convergence of relative frequencies of events to their probabilities
    • Vapnik, V., Chervonenkis, A., 1971. On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16, 264-280.
    • (1971) Theory Probab. Appl. , vol.16 , pp. 264-280
    • Vapnik, V.1    Chervonenkis, A.2
  • 16
    • 0001742955 scopus 로고
    • Weak convergence of smoothed empirical processes
    • van der Vaart, A., 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.1
  • 17
    • 0003679019 scopus 로고    scopus 로고
    • Weak Convergence and Empirical Processes
    • Springer, Berlin
    • van der Vaart, A., Wellner, J., 1996. Weak Convergence and Empirical Processes. Springer, Berlin.
    • (1996)
    • van der Vaart, A.1    Wellner, J.2
  • 18
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.