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Volumn 9, Issue 5, 2003, Pages 783-807

On adaptive inverse estimation of linear functional in Hilbert scales

Author keywords

Adaptive estimation; Hilbert scales; Inverse problems; Linear functionals; Minimax risk; Regularization

Indexed keywords


EID: 33747349217     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1066418878     Document Type: Article
Times cited : (25)

References (26)
  • 1
    • 0030327799 scopus 로고    scopus 로고
    • A constrained risk inequality with application to nonparametric estimation
    • Brown, L. and Low, M.G. (1996) A constrained risk inequality with application to nonparametric estimation. Ann. Statist., 24, 2524-2535.
    • (1996) Ann. Statist. , vol.24 , pp. 2524-2535
    • Brown, L.1    Low, M.G.2
  • 2
    • 0036022583 scopus 로고    scopus 로고
    • Sharp adaptation for inverse problems with random noise
    • Cavalier, L. and Tsybakov, A. (2002) Sharp adaptation for inverse problems with random noise. Probab. Theory Related Fields, 123, 323-354.
    • (2002) Probab. Theory Related Fields , vol.123 , pp. 323-354
    • Cavalier, L.1    Tsybakov, A.2
  • 3
    • 21344492321 scopus 로고
    • Statistical estimation and optimal recovery
    • Donoho, D.L. (1994) Statistical estimation and optimal recovery. Ann. Statist., 22, 238-270.
    • (1994) Ann. Statist. , vol.22 , pp. 238-270
    • Donoho, D.L.1
  • 4
    • 0001573354 scopus 로고
    • Renormalization exponents and optimal pointwise rates of convergence
    • Donoho, D. and Low, M. (1992) Renormalization exponents and optimal pointwise rates of convergence. Ann. Statist., 20, 944-970.
    • (1992) Ann. Statist. , vol.20 , pp. 944-970
    • Donoho, D.1    Low, M.2
  • 5
    • 0034561754 scopus 로고    scopus 로고
    • Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations
    • Goldenshluger, A. and Pereverzev, S.V. (2000) Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations. Probab. Theory Related Fields, 118, 169-186.
    • (2000) Probab. Theory Related Fields , vol.118 , pp. 169-186
    • Goldenshluger, A.1    Pereverzev, S.V.2
  • 6
    • 0000554469 scopus 로고
    • Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization
    • Hegland, M. (1995) Variable Hilbert scales and their interpolation inequalities with applications to Tikhonov regularization. Appl. Anal., 59, 207-223.
    • (1995) Appl. Anal. , vol.59 , pp. 207-223
    • Hegland, M.1
  • 7
    • 0002282584 scopus 로고
    • On nonparametric estimation of the value of a linear functional in Gaussian white noise
    • Ibragimov, I.A. and Khas'minskii, R.Z. (1984) On nonparametric estimation of the value of a linear functional in Gaussian white noise. Theory Probab. Appl., 29, 18-32.
    • (1984) Theory Probab. Appl. , vol.29 , pp. 18-32
    • Ibragimov, I.A.1    Khas'minskii, R.Z.2
  • 8
    • 0007252424 scopus 로고
    • Estimation of linear functionals in Gaussian noise
    • Ibragimov, I.A. and Khas'minskii, R.Z. (1987) Estimation of linear functionals in Gaussian noise. Theory Probab. Appl., 32, 30-39.
    • (1987) Theory Probab. Appl. , vol.32 , pp. 30-39
    • Ibragimov, I.A.1    Khas'minskii, R.Z.2
  • 10
    • 0000012624 scopus 로고
    • A problem of adaptive estimation in Gaussian white noise
    • Lepski, O. (1990) A problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl., 36, 454-466.
    • (1990) Theory Probab. Appl. , vol.36 , pp. 454-466
    • Lepski, O.1
  • 11
    • 0001066342 scopus 로고
    • Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates
    • Lepski, O. (1991) Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates. Theory Probab. Appl., 36, 682-697.
    • (1991) Theory Probab. Appl. , vol.36 , pp. 682-697
    • Lepski, O.1
  • 12
    • 0007267891 scopus 로고
    • Asymptotically minimax adaptive estimation II: Schemes without optimal adaptation. Adaptive estimators
    • Lepski, O. (1992) Asymptotically minimax adaptive estimation II: Schemes without optimal adaptation. Adaptive estimators. Theory Probab. Appl., 37, 433-448.
    • (1992) Theory Probab. Appl. , vol.37 , pp. 433-448
    • Lepski, O.1
  • 13
    • 0030269038 scopus 로고    scopus 로고
    • Statistical inverse estimation in Hilbert scales
    • Mair, B.A. and Ruymgaart, F.H. (1996) Statistical inverse estimation in Hilbert scales. SIAM J. Appl. Math., 56, 1424-1444.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1424-1444
    • Mair, B.A.1    Ruymgaart, F.H.2
  • 14
    • 0034580744 scopus 로고    scopus 로고
    • Optimal discretization of inverse problems in Hilbert scales. Regularization and self-regularization of projection methods
    • Mathé, P. and Pereverzev, S.V (2001) Optimal discretization of inverse problems in Hilbert scales. Regularization and self-regularization of projection methods. SIAM J. Numer. Anal., 38, 1999-2021.
    • (2001) SIAM J. Numer. Anal. , vol.38 , pp. 1999-2021
    • Mathé, P.1    Pereverzev, S.V.2
  • 15
    • 84951418001 scopus 로고
    • Error bounds for Tikhonov regularization in Hilbert scales
    • Natterer, F. (1984) Error bounds for Tikhonov regularization in Hilbert scales. Appl. Anal., 19, 29-37.
    • (1984) Appl. Anal. , vol.19 , pp. 29-37
    • Natterer, F.1
  • 16
    • 0001504070 scopus 로고
    • On a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates
    • Neubauer, A. (1988) On a posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates. SIAM J. Numer. Anal., 25, 1313-1326.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1313-1326
    • Neubauer, A.1
  • 17
    • 0004865563 scopus 로고    scopus 로고
    • On converse and saturation results for Tikhonov regularization of linear ill-posed problems
    • Neubauer, A. (1997) On converse and saturation results for Tikhonov regularization of linear ill-posed problems. SIAM J. Numer. Anal., 34, 517-527.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 517-527
    • Neubauer, A.1
  • 20
    • 0000874622 scopus 로고
    • A unified approach to inversion problems in statistics
    • Ruymgaart, F.H. (1993) A unified approach to inversion problems in statistics. Math. Methods Statist., 2, 130-146.
    • (1993) Math. Methods Statist. , vol.2 , pp. 130-146
    • Ruymgaart, F.H.1
  • 22
    • 0000414254 scopus 로고    scopus 로고
    • Error estimates for regularization methods in Hilbert scales
    • Tautenhahn, U. (1996) Error estimates for regularization methods in Hilbert scales. SIAM J. Numer. Anal., 33, 2120-2130.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 2120-2130
    • Tautenhahn, U.1
  • 24
    • 0013286501 scopus 로고
    • Projection methods and self-regularization of ill-posed problems
    • Vainikko, G.M. and Hämarik, U.A. (1985) Projection methods and self-regularization of ill-posed problems. Izv. Vyssh. Uchebn. Zaved. Mat., 29, 1-17.
    • (1985) Izv. Vyssh. Uchebn. Zaved. Mat. , vol.29 , pp. 1-17
    • Vainikko, G.M.1    Hämarik, U.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.