메뉴 건너뛰기




Volumn 13, Issue 4, 2007, Pages 481-496

On an exponential bound for the Kaplan-Meier estimator

Author keywords

Confidence bands; Empirical distribution; Inequalities; Product limit estimator; Random censoring; Right censoring; Uniform limit theorems; Universal limit theorems

Indexed keywords

ARTICLE; COMPUTER SIMULATION; HUMAN; KAPLAN MEIER METHOD; MONTE CARLO METHOD; STATISTICAL ANALYSIS;

EID: 37649015731     PISSN: 13807870     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10985-007-9055-z     Document Type: Article
Times cited : (11)

References (36)
  • 2
    • 0033227358 scopus 로고    scopus 로고
    • A Dvoretzky-Kiefer-Wolfowitz type inequality for the Kaplan- Meier estimator
    • Bitouzé D, Laurent B and Massart P (1999). A Dvoretzky-Kiefer- Wolfowitz type inequality for the Kaplan- Meier estimator. Ann Inst H Poincar Probabé Stat 35: 735-763
    • (1999) Ann Inst H Poincar Probabé Stat , vol.35 , pp. 735-763
    • Bitouzé, D.1    Laurent, B.2    Massart, P.3
  • 3
    • 0001682292 scopus 로고
    • A large sample study of the life table and product limit estimates under random censorship
    • Breslow N and Crowley J (1974). A large sample study of the life table and product limit estimates under random censorship. Ann Stat 2: 437-453
    • (1974) Ann Stat , vol.2 , pp. 437-453
    • Breslow, N.1    Crowley, J.2
  • 4
    • 0002688167 scopus 로고
    • Strong approximations of some biometric estimates under random censorship
    • Burke MD, Csörgo S and Horváth L (1981). Strong approximations of some biometric estimates under random censorship. Z Wahrsch Verw Gebiete 56: 87-112
    • (1981) Z Wahrsch Verw Gebiete , vol.56 , pp. 87-112
    • Burke, M.D.1    Csörgo, S.2    Horváth, L.3
  • 5
    • 0030510645 scopus 로고    scopus 로고
    • A counterexample to a conjecture concerning the Hall-Wellner band
    • Chen K and Ying Z (1996). A counterexample to a conjecture concerning the Hall-Wellner band. Ann Stat 24: 641-646
    • (1996) Ann Stat , vol.24 , pp. 641-646
    • Chen, K.1    Ying, Z.2
  • 6
    • 0039470129 scopus 로고    scopus 로고
    • Universal Gaussian approximations under random censorship
    • Csörgo S (1996). Universal Gaussian approximations under random censorship. Ann Stat 24: 2744-2778
    • (1996) Ann Stat , vol.24 , pp. 2744-2778
    • Csörgo, S.1
  • 7
    • 0001009084 scopus 로고
    • The rate of strong uniform consistency for the product-limit estimator
    • Csörgo S and Horváth L (1983). The rate of strong uniform consistency for the product-limit estimator. Z Wahrsch Verw Gebiete 62: 411-426
    • (1983) Z Wahrsch Verw Gebiete , vol.62 , pp. 411-426
    • Csörgo, S.1    Horváth, L.2
  • 8
    • 84988058947 scopus 로고
    • Confidence bands from censored samples
    • Csörgo S and Horváth L (1986). Confidence bands from censored samples. Canad J Stat 14: 131-144
    • (1986) Canad J Stat , vol.14 , pp. 131-144
    • Csörgo, S.1    Horváth, L.2
  • 9
    • 0001529786 scopus 로고
    • Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator
    • Dvoretzky A, Kiefer J and Wolfowitz J (1956). Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann Math Stat 27: 642-669
    • (1956) Ann Math Stat , vol.27 , pp. 642-669
    • Dvoretzky, A.1    Kiefer, J.2    Wolfowitz, J.3
  • 10
    • 0003104081 scopus 로고
    • Censoring and stochastic integrals
    • Mathematisch Centrum, Amsterdam
    • Gill RD (1980) Censoring and stochastic integrals, vol. 124 of Mathematical Centre Tracts. Mathematisch Centrum, Amsterdam
    • (1980) Mathematical Centre Tracts , vol.124
    • Gill, R.D.1
  • 11
    • 0002761375 scopus 로고
    • Large sample behaviour of the product-limit estimator on the whole line
    • Gill R (1983). Large sample behaviour of the product-limit estimator on the whole line. Ann Stat 11: 49-58
    • (1983) Ann Stat , vol.11 , pp. 49-58
    • Gill, R.1
  • 12
    • 0002980330 scopus 로고
    • Glivenko-Cantelli for Kaplan-Meier
    • Gill RD (1994). Glivenko-Cantelli for Kaplan-Meier. Math Methods Stat 3: 76-87
    • (1994) Math Methods Stat , vol.3 , pp. 76-87
    • Gill, R.D.1
  • 13
    • 0642329269 scopus 로고
    • Confidence bands for the Kaplan-Meier survival curve estimate
    • Gillespie MJ and Fisher L (1979). Confidence bands for the Kaplan-Meier survival curve estimate. Ann Stat 7: 920-924
    • (1979) Ann Stat , vol.7 , pp. 920-924
    • Gillespie, M.J.1    Fisher, L.2
  • 14
    • 0033233678 scopus 로고    scopus 로고
    • Laws of the iterated logarithm for censored data
    • Giné E and Guillou A (1999). Laws of the iterated logarithm for censored data. Ann Probab 27: 2042-2067
    • (1999) Ann Probab , vol.27 , pp. 2042-2067
    • Giné, E.1    Guillou, A.2
  • 15
    • 0039196168 scopus 로고
    • The Chung-Smirnov law for the product-limit estimator under random censorship
    • Gu M (1991) The Chung-Smirnov law for the product-limit estimator under random censorship. Chin. Ann Math Ser B 12:96-105.
    • (1991) Chin. Ann Math ser B , vol.12 , pp. 96-105
    • Gu, M.1
  • 16
    • 37649003140 scopus 로고    scopus 로고
    • A Chinese summary appears
    • A Chinese summary appears in Chin Ann Math Ser A 12(1):119
    • Chin Ann Math ser A , vol.12 , Issue.1 , pp. 119
  • 17
    • 0000813892 scopus 로고
    • Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncation
    • Gu MG and Lai TL (1990). Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncation. Ann Probab 18: 160-189
    • (1990) Ann Probab , vol.18 , pp. 160-189
    • Gu, M.G.1    Lai, T.L.2
  • 18
    • 0018894430 scopus 로고
    • Confidence bands for a survival curve from censored data
    • Hall WJ and Wellner JA (1980). Confidence bands for a survival curve from censored data. Biometrika 67: 133-143
    • (1980) Biometrika , vol.67 , pp. 133-143
    • Hall, W.J.1    Wellner, J.A.2
  • 19
    • 0031476666 scopus 로고    scopus 로고
    • Likelihood ratio-based confidence bands for survival functions
    • Hollander M, McKeague IW and Yang J (1997). Likelihood ratio-based confidence bands for survival functions. J Am Stat Assoc 92: 215-226
    • (1997) J Am Stat Assoc , vol.92 , pp. 215-226
    • Hollander, M.1    Yang, J.2
  • 20
    • 84988112579 scopus 로고
    • Families of confidence bands for the survival function under the general random censorship model and the Koziol-Green model
    • Hollander M and Peña E (1989). Families of confidence bands for the survival function under the general random censorship model and the Koziol-Green model. Can J Stat 17: 59-74
    • (1989) Can J Stat , vol.17 , pp. 59-74
    • Hollander, M.1    Peña, E.2
  • 21
    • 33845382806 scopus 로고
    • Nonparametric estimation from incomplete observations
    • Kaplan EL and Meier P (1958). Nonparametric estimation from incomplete observations. J Am Stat Assoc 53: 457-481
    • (1958) J Am Stat Assoc , vol.53 , pp. 457-481
    • Kaplan, E.L.1    Meier, P.2
  • 22
    • 0000506938 scopus 로고
    • The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
    • Massart P (1990). The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Ann Probab 18: 1269-1283
    • (1990) Ann Probab , vol.18 , pp. 1269-1283
    • Massart, P.1
  • 23
    • 31044442381 scopus 로고    scopus 로고
    • Width-scaled confidence bands for survival functions
    • McKeague IW and Zhao Y (2006). Width-scaled confidence bands for survival functions. Stat Probab Lett 76: 327-339
    • (2006) Stat Probab Lett , vol.76 , pp. 327-339
    • Zhao, Y.1
  • 24
    • 0038411416 scopus 로고
    • Estimation of a distribution function from incomplete observations
    • Perspectives in probability and statistics (papers in honour of M. S. Bartlett on the occasion of his 65th birthday) Univ. Sheffield, Sheffield
    • Meier, P (1975) Estimation of a distribution function from incomplete observations. In Perspectives in probability and statistics (papers in honour of M. S. Bartlett on the occasion of his 65th birthday). Applied Probability Trust, Univ. Sheffield, Sheffield, pp. 67-87
    • (1975) Applied Probability Trust , pp. 67-87
    • Meier, P.1
  • 25
    • 0005998423 scopus 로고
    • Plots and tests for goodness of fit with randomly censored data
    • Nair VN (1981). Plots and tests for goodness of fit with randomly censored data. Biometrika 68: 99-103
    • (1981) Biometrika , vol.68 , pp. 99-103
    • Nair, V.N.1
  • 28
    • 38149147614 scopus 로고
    • Convergence of the Kaplan-Meier estimator in weighted sup-norms
    • Stute W (1994). Convergence of the Kaplan-Meier estimator in weighted sup-norms. Stat Probab Lett 20: 219-223
    • (1994) Stat Probab Lett , vol.20 , pp. 219-223
    • Stute, W.1
  • 29
    • 0000424171 scopus 로고
    • Strong and weak representations of cumulative hazard function and Kaplan-Meier estimators on increasing sets
    • Stute W (1994). Strong and weak representations of cumulative hazard function and Kaplan-Meier estimators on increasing sets. J Stat Plan Inference 42: 315-329
    • (1994) J Stat Plan Inference , vol.42 , pp. 315-329
    • Stute, W.1
  • 30
    • 0009936695 scopus 로고
    • The strong law under random censorship
    • Stute W and Wang J-L (1993). The strong law under random censorship. Ann Stat 21: 1591-1607
    • (1993) Ann Stat , vol.21 , pp. 1591-1607
    • Stute, W.1    Wang, J.-L.2
  • 32
    • 21144465429 scopus 로고
    • Hellinger-consistency of certain nonparametric maximum likelihood estimators
    • van de Geer S (1993). Hellinger-consistency of certain nonparametric maximum likelihood estimators. Ann Stat 21: 14-44
    • (1993) Ann Stat , vol.21 , pp. 14-44
    • Van De Geer, S.1
  • 34
    • 0003679019 scopus 로고    scopus 로고
    • Weak convergence and empirical processes
    • Springer-Verlag, New York. With applications to statistics
    • van der Vaart AW, Wellner JA (1996) Weak convergence and empirical processes. Springer Series in Statistics, Springer-Verlag, New York. With applications to statistics
    • (1996) Springer Series in Statistics
    • Van Der Vaart, A.W.1    Wellner, J.A.2
  • 35
    • 0000383087 scopus 로고
    • A note on the uniform consistency of the Kaplan-Meier estimator
    • Wang JG (1987). A note on the uniform consistency of the Kaplan-Meier estimator. Ann Stat 15: 1313-1316
    • (1987) Ann Stat , vol.15 , pp. 1313-1316
    • Wang, J.G.1
  • 36
    • 38249023918 scopus 로고
    • A note on the asymptotic properties of the product-limit estimator on the whole line
    • Ying Z (1989). A note on the asymptotic properties of the product-limit estimator on the whole line. Stat Probab Lett 7: 311-314
    • (1989) Stat Probab Lett , vol.7 , pp. 311-314
    • Ying, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.