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Volumn 33, Issue 3, 2005, Pages 1330-1356

Estimation of a function under shape restrictions. Applications to reliability

(1)  Reboul, L a,b  

b NONE   (France)

Author keywords

Adaptive estimation; Data driven estimator; Hazard rate; Nonhomogeneous Poisson process; U shaped function; Unimodal function; Variable binwidth histogram

Indexed keywords


EID: 23744513170     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000138     Document Type: Article
Times cited : (20)

References (33)
  • 3
    • 0008233557 scopus 로고
    • Some nonparametric techniques for estimating the intensity function of a cancer related nonstationary Poisson process
    • BARTOSZYŃSKI, R., BROWN, B. W., MCBRIDE, C. M. and THOMPSON, J. R. (1981). Some nonparametric techniques for estimating the intensity function of a cancer related nonstationary Poisson process. Ann. Statist. 9 1050-1060.
    • (1981) Ann. Statist. , vol.9 , pp. 1050-1060
    • Bartoszyński, R.1    Brown, B.W.2    Mcbride, C.M.3    Thompson, J.R.4
  • 4
    • 0040795081 scopus 로고
    • Robust estimation of unimodal densities
    • Univ. Paris X-Nanterre
    • BIRGÉ, L. (1987). Robust estimation of unimodal densities. Technical report, Univ. Paris X-Nanterre.
    • (1987) Technical Report
    • Birgé, L.1
  • 5
    • 0038243770 scopus 로고
    • On the risk of histograms for estimating decreasing densities
    • BIRGÉ, L. (1987). On the risk of histograms for estimating decreasing densities. Ann. Statist. 15 1013-1022.
    • (1987) Ann. Statist. , vol.15 , pp. 1013-1022
    • Birgé, L.1
  • 6
    • 0000513614 scopus 로고
    • The Grenander estimator: A nonasymptotic approach
    • BIRGE, L. (1989). The Grenander estimator: A nonasymptotic approach. Ann. Statist. 17 1532-1549.
    • (1989) Ann. Statist. , vol.17 , pp. 1532-1549
    • Birge, L.1
  • 7
    • 0031494445 scopus 로고    scopus 로고
    • Estimation of unimodal densities without smoothness assumptions
    • BIRGÉ, L. (1997). Estimation of unimodal densities without smoothness assumptions. Ann. Statist. 25 970-981.
    • (1997) Ann. Statist. , vol.25 , pp. 970-981
    • Birgé, L.1
  • 8
    • 0001772469 scopus 로고
    • Estimation of isotonic regression
    • (M. L. Puri, ed.). Cambridge Univ. Press, London
    • BRUNK, H. D. (1970). Estimation of isotonic regression. In Nonparametric Techniques in Statistical Inference (M. L. Puri, ed.) 177-197. Cambridge Univ. Press, London.
    • (1970) Nonparametric Techniques in Statistical Inference , pp. 177-197
    • Brunk, H.D.1
  • 9
    • 0001215143 scopus 로고
    • Evaluation of an unknown distribution density from observations
    • CENCOV, N. N. (1962). Evaluation of an unknown distribution density from observations. Soviet Math. Dokl. 3 1559-1562.
    • (1962) Soviet Math. Dokl. , vol.3 , pp. 1559-1562
    • Cencov, N.N.1
  • 10
    • 23744476626 scopus 로고
    • Bayes linear estimators of the intensity function of the nonstationary Poisson process
    • CLEVENSON, M. L. and ZIDEK, J. V. (1977). Bayes linear estimators of the intensity function of the nonstationary Poisson process. J. Amer. Statist. Assoc. 72 112-120.
    • (1977) J. Amer. Statist. Assoc. , vol.72 , pp. 112-120
    • Clevenson, M.L.1    Zidek, J.V.2
  • 14
    • 0036003098 scopus 로고    scopus 로고
    • Sharp asymptotics for isotonic regression
    • DUROT, C. (2002). Sharp asymptotics for isotonic regression. Probab. Theory Related Fields 122 222-240.
    • (2002) Probab. Theory Related Fields , vol.122 , pp. 222-240
    • Durot, C.1
  • 15
    • 84945603474 scopus 로고
    • On the theory of mortality measurement
    • GRENANDER, U. (1956). On the theory of mortality measurement. II. Skand.-Aktuarietidskr. 39 125-153.
    • (1956) II. Skand.-Aktuarietidskr. , vol.39 , pp. 125-153
    • Grenander, U.1
  • 16
    • 0001082027 scopus 로고
    • Estimating a monotone density
    • (L. M. Le Cam and R. A. Olshen, eds.). Wadsworth, Monterey, CA
    • GROENEBOOM, P. (1985). Estimating a monotone density. In Proc. Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (L. M. Le Cam and R. A. Olshen, eds.) 2 539-555. Wadsworth, Monterey, CA.
    • (1985) Proc. Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer , vol.2 , pp. 539-555
    • Groeneboom, P.1
  • 18
    • 33845382806 scopus 로고
    • Nonparametric estimation from incomplete observations
    • KAPLAN, E. L. and MEIER, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457-481.
    • (1958) J. Amer. Statist. Assoc. , vol.53 , pp. 457-481
    • Kaplan, E.L.1    Meier, P.2
  • 19
    • 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 1520-1535.
    • (1987) Ann. Statist. , vol.15 , pp. 1520-1535
    • Marron, J.S.1    Padgett, W.J.2
  • 20
    • 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
  • 22
    • 0028224335 scopus 로고
    • Hazard rate estimation under random censoring with varying kernels and bandwidths
    • MÜLLER, H.-G. and WANG, J.-L. (1994). Hazard rate estimation under random censoring with varying kernels and bandwidths. Biometrics 50 61-76.
    • (1994) Biometrics , vol.50 , pp. 61-76
    • Müller, H.-G.1    Wang, J.-L.2
  • 23
    • 84952143251 scopus 로고
    • Theory and applications of hazard plotting for censured failure data
    • NELSON, W. (1972). Theory and applications of hazard plotting for censured failure data. Technometrics 14 945-966.
    • (1972) Technometrics , vol.14 , pp. 945-966
    • Nelson, W.1
  • 24
    • 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 1065-1076.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 1065-1076
    • Parzen, E.1
  • 26
    • 0002369909 scopus 로고
    • Empirical choice of histograms and kernel density estimators
    • RUDEMO, M. (1982). Empirical choice of histograms and kernel density estimators. Scand. J. Statist. 9 65-78.
    • (1982) Scand. J. Statist. , vol.9 , pp. 65-78
    • Rudemo, M.1
  • 28
    • 0010807006 scopus 로고
    • Estimation of the failure rate. A survey of nonparametric methods. I. Non-Bayesian methods
    • SINGPURWALLA, N. D. and WONG, M. Y. (1983). Estimation of the failure rate. A survey of nonparametric methods. I. Non-Bayesian methods. Comm. Statist. Theory Methods 12 559-588.
    • (1983) Comm. Statist. Theory Methods , vol.12 , pp. 559-588
    • Singpurwalla, N.D.1    Wong, M.Y.2
  • 29
    • 0001048793 scopus 로고
    • An asymptotically optimal window selection rule for kernel density estimates
    • STONE, C. J. (1984). An asymptotically optimal window selection rule for kernel density estimates. Ann. Statist. 12 1285-1297.
    • (1984) Ann. Statist. , vol.12 , pp. 1285-1297
    • Stone, C.J.1
  • 30
    • 0000467040 scopus 로고
    • The estimation of the hazard function from randomly censored data by the kernel method
    • TANNER, M. A. and WONG, W. H. (1983). The estimation of the hazard function from randomly censored data by the kernel method. Ann. Statist. 11 989-993.
    • (1983) Ann. Statist. , vol.11 , pp. 989-993
    • Tanner, M.A.1    Wong, W.H.2
  • 31
    • 0000024854 scopus 로고
    • 1 theory of estimation of monotone and unimodal densities
    • 1 theory of estimation of monotone and unimodal densities. J. Nonparametr. Statist. 4 249-261.
    • (1995) J. Nonparametr. Statist. , vol.4 , pp. 249-261
    • Wang, Y.1
  • 32
    • 0000477412 scopus 로고
    • Maximum likelihood estimation of a unimodal density function
    • WEGMAN, E. J. (1970). Maximum likelihood estimation of a unimodal density function. Ann. Math. Statist. 41 457-471.
    • (1970) Ann. Math. Statist. , vol.41 , pp. 457-471
    • Wegman, E.J.1
  • 33
    • 0001218245 scopus 로고
    • Nonparametric inference for rates with censored survival data
    • YANDELL, B. S. (1983). Nonparametric inference for rates with censored survival data. Ann. Statist. 11 1119-1135.
    • (1983) Ann. Statist. , vol.11 , pp. 1119-1135
    • Yandell, B.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.