메뉴 건너뛰기




Volumn 27, Issue 12, 1998, Pages 2909-2924

On the asymptotic normality of the kernel estimators of the density function and its derivatives under censoring

Author keywords

Asymptotic normality; Censored data; Consistency; Density; Derivative; Kaplan Meier estimator; Kernel estimator; Mode

Indexed keywords


EID: 0009908271     PISSN: 03610926     EISSN: None     Source Type: Journal    
DOI: 10.1080/03610929808832263     Document Type: Article
Times cited : (15)

References (29)
  • 1
    • 0001281940 scopus 로고
    • Maxima! deviation theory of density and failure rate function estimates based on censored data
    • (P.R. Krishnaiah ed.), North-Holland, New York
    • Blum J.R. and Susarla V. (1980) : Maxima! deviation theory of density and failure rate function estimates based on censored data. In Multivariate analysis 5 (P.R. Krishnaiah ed.), p. 213-222, North-Holland, New York.
    • (1980) Multivariate Analysis , vol.5 , pp. 213-222
    • Blum, J.R.1    Susarla, V.2
  • 2
    • 0000787802 scopus 로고
    • Bandwidth selection for kernel density estimation
    • Chiu S.T. (1991) : Bandwidth selection for kernel density estimation. Ann. Statist., 19, p. 1883-1905.
    • (1991) Ann. Statist. , vol.19 , pp. 1883-1905
    • Chiu, S.T.1
  • 3
    • 0001538747 scopus 로고    scopus 로고
    • On pseudodata methods for removing boundary effects in kernel density estimation
    • Cowling A. and Hall P. (1996) : On pseudodata methods for removing boundary effects in kernel density estimation. J. R. Statist. Soc. B, 58, p. 551-563.
    • (1996) J. R. Statist. Soc. B , vol.58 , pp. 551-563
    • Cowling, A.1    Hall, P.2
  • 4
    • 0001618486 scopus 로고
    • Optimum kernel estimators of the mode
    • Eddy W.F. (1980) : Optimum kernel estimators of the mode. Ann. Statist., 8, p. 870-882.
    • (1980) Ann. Statist. , vol.8 , pp. 870-882
    • Eddy, W.F.1
  • 5
    • 0000748586 scopus 로고
    • The asymptotic distributions of kernel estimators the mode
    • Eddy W.F. (1982) : The asymptotic distributions of kernel estimators the mode. Z. Wahrsch. Verw. Gebiete, 59, p. 279-290.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.59 , pp. 279-290
    • Eddy, W.F.1
  • 6
    • 0001104182 scopus 로고
    • The two sample problem with censored data
    • Univ. California Press
    • Efron B. (1967) : The two sample problem with censored data. Proc. Fifth Berkley Symp. Math. Statist. Probab. 4, p. 831-853. Univ. California Press.
    • (1967) Proc. Fifth Berkley Symp. Math. Statist. Probab. , vol.4 , pp. 831-853
    • Efron, B.1
  • 7
    • 0000665083 scopus 로고
    • Nonparametric estimation of a multidimensional probability density
    • Epanechnikov V.A. (1969) : Nonparametric estimation of a multidimensional probability density. Theory Probab. Appl. 14, 153-158.
    • (1969) Theory Probab. Appl. , vol.14 , pp. 153-158
    • Epanechnikov, V.A.1
  • 8
    • 0042214129 scopus 로고
    • Stong consistency properties of nonparametric estimators for randomly censored data, I : Estimation of density and failure rate
    • Földes A., Rejto L. and Winter B.B. (1981) : Stong consistency properties of nonparametric estimators for randomly censored data, I : Estimation of density and failure rate. Periodica Mathematica Hungarica, 11, p. 233-250.
    • (1981) Periodica Mathematica Hungarica , vol.11 , pp. 233-250
    • Földes, A.1    Rejto, L.2    Winter, B.B.3
  • 9
    • 0002229220 scopus 로고
    • Stong consistency properties of nonparametric estimators for randomly censored data, II : Estimation of density and failure rate
    • Földes A., Rejto L. and Winter B.B. (1981) : Stong consistency properties of nonparametric estimators for randomly censored data, II : Estimation of density and failure rate. Periodica Mathematica Hungarica, 12, p. 15-29.
    • (1981) Periodica Mathematica Hungarica , vol.12 , pp. 15-29
    • Földes, A.1    Rejto, L.2    Winter, B.B.3
  • 10
    • 33845382806 scopus 로고
    • Nonparametric estimation from incomplete observations
    • Kaplan E.I. and Meier P. (1958) : Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc., 53, p. 457-481.
    • (1958) J. Amer. Statist. Assoc. , vol.53 , pp. 457-481
    • Kaplan, E.I.1    Meier, P.2
  • 11
    • 84988112849 scopus 로고
    • Weak and strong uniform consistency rates of kernel density estimates for randomly censored data
    • Karunamuni R.J. and Song Yang (1991) : Weak and strong uniform consistency rates of kernel density estimates for randomly censored data. Canad. J. Statist., 19, p. 349-359.
    • (1991) Canad. J. Statist. , vol.19 , pp. 349-359
    • Karunamuni, R.J.1    Song, Y.2
  • 12
    • 0001254816 scopus 로고
    • Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator
    • Lo S.H., Mack Y.P. and Wang J.L. (1989) : Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator. Prob. Th. Rel. Fields, 80, p. 461-473.
    • (1989) Prob. Th. Rel. Fields , vol.80 , pp. 461-473
    • Lo, S.H.1    Mack, Y.P.2    Wang, J.L.3
  • 13
    • 26844563919 scopus 로고    scopus 로고
    • Asymptotic normality of kernel estimators of the conditional mode under strong mixing hypothesis
    • Louani D. and Ould Said E. (1996) : Asymptotic normality of kernel estimators of the conditional mode under strong mixing hypothesis. Technical Report No 21, Université du Littoral.
    • (1996) Technical Report No 21, Université du Littoral
    • Louani, D.1    Ould Said, E.2
  • 14
    • 85034180309 scopus 로고
    • Van Nostrand-Reinhold, Princeton, New Jersey
    • Loeve M. (1963) : Probability Theory. 2nd Edit., Van Nostrand-Reinhold, Princeton, New Jersey.
    • (1963) Probability Theory. 2nd Edit.
    • Loeve, M.1
  • 15
    • 0001354397 scopus 로고
    • Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples
    • Marron J.S. and Padgett W.J. (1987) : Asymptotically optimal bandwidth selection for kernel density estimators from randomly right-censored samples. Ann. Statist., 15, p. 1520-1535.
    • (1987) Ann. Statist. , vol.15 , pp. 1520-1535
    • Marron, J.S.1    Padgett, W.J.2
  • 16
    • 0000395261 scopus 로고
    • Some asymptotic properties of kernel estimators of a density function in case of censored data
    • Mielniczuk J. (1986) : Some asymptotic properties of kernel estimators of a density function in case of censored data. Ann. Statist., 14, p. 766-773.
    • (1986) Ann. Statist. , vol.14 , pp. 766-773
    • Mielniczuk, J.1
  • 17
    • 84948235172 scopus 로고
    • Nonparametric density estimation from censored data
    • Padgett W.J. and Mc Nichols D.T. (1984) : Nonparametric density estimation from censored data. Comm. Statist. Theory Meth., 13, p. 1815-1842.
    • (1984) Comm. Statist. Theory Meth. , vol.13 , pp. 1815-1842
    • Padgett, W.J.1    Mc Nichols, D.T.2
  • 18
    • 0002780488 scopus 로고
    • Comparison of data-driven bandwidth selectors
    • Park B. and Marron J.S. (1990) : Comparison of data-driven bandwidth selectors. J. Amer. Statist. Assoc., 85, p. 66-72.
    • (1990) J. Amer. Statist. Assoc. , vol.85 , pp. 66-72
    • Park, B.1    Marron, J.S.2
  • 19
    • 0001473437 scopus 로고
    • On estimation of a probability density function and mode
    • Parzen E. (1962) : On estimation of a probability density function and mode. Ann. Math. Statist., 33, p. 1065-1076.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 20
    • 21344480142 scopus 로고
    • On the least squares cross-validation bandwidth in hazard rate estimation
    • Patil P.N. (1993) : On the least squares cross-validation bandwidth in hazard rate estimation. Ann. Statist. 21, p. 1792-1810.
    • (1993) Ann. Statist. , vol.21 , pp. 1792-1810
    • Patil, P.N.1
  • 22
    • 0000060892 scopus 로고
    • Nonparametric estimation of the mode of a multivariate density
    • Samanta M. (1973) : Nonparametric estimation of the mode of a multivariate density. South African Statist. J., 7, p. 109-117.
    • (1973) South African Statist. J. , vol.7 , pp. 109-117
    • Samanta, M.1
  • 23
    • 0001646977 scopus 로고
    • Nonparametric estimation of the conditional mode
    • Samanta M. and Thavaneswaran A. (1990) : Nonparametric estimation of the conditional mode. Comm. Statist. Theo. Meth., 16, p. 4515-4524.
    • (1990) Comm. Statist. Theo. Meth. , vol.16 , pp. 4515-4524
    • Samanta, M.1    Thavaneswaran, A.2
  • 24
    • 84948304931 scopus 로고
    • Incorporating support contraints into nonparametric estimators of densities
    • Schuster E.F. (1985) : Incorporating support contraints into nonparametric estimators of densities. Comm. Statist. Theor. Meth., 14, p. 1123-1136.
    • (1985) Comm. Statist. Theor. Meth. , vol.14 , pp. 1123-1136
    • Schuster, E.F.1
  • 25
    • 84935473220 scopus 로고
    • Biased and unbiased cross-validation in density estimation
    • Scott D.W. and Terrell G.R. (1987) : Biased and unbiased cross-validation in density estimation. J. Amer. Statist. Assoc., 82, p. 1131-1146.
    • (1987) J. Amer. Statist. Assoc. , vol.82 , pp. 1131-1146
    • Scott, D.W.1    Terrell, G.R.2
  • 27
    • 0018372982 scopus 로고
    • Mean squared errors of estimates of a density and its derivatives
    • Singh (1979) : Mean squared errors of estimates of a density and its derivatives. Biometrika, 66, p. 177-180.
    • (1979) Biometrika , vol.66 , pp. 177-180
    • Singh1
  • 28
    • 21844495989 scopus 로고
    • The central limit theorem under random censorship
    • Stute W. (1995) : The central limit theorem under random censorship. Ann. Statist., 23, p. 422-439.
    • (1995) Ann. Statist. , vol.23 , pp. 422-439
    • Stute, W.1
  • 29
    • 0000667620 scopus 로고
    • On strong consistency of density estimates
    • Van Ryzin J. (1969) : On strong consistency of density estimates. Ann. Math. Statist., 40, p. 1765-1772.
    • (1969) Ann. Math. Statist. , vol.40 , pp. 1765-1772
    • Van Ryzin, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.