메뉴 건너뛰기




Volumn 20, Issue 6, 2004, Pages 1773-1789

Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETIC WAVE SCATTERING; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NONLINEAR SYSTEMS; POLYNOMIALS; PROBLEM SOLVING;

EID: 10844236506     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/20/6/005     Document Type: Article
Times cited : (74)

References (40)
  • 2
    • 0013178793 scopus 로고
    • Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion
    • Bakushinskii A B 1984 Remarks on choosing a regularization parameter using the quasi-optimality and ratio criterion USSR Comput. Math. Phys. 24 181-2
    • (1984) USSR Comput. Math. Phys. , vol.24 , pp. 181-182
    • Bakushinskii, A.B.1
  • 4
    • 18244372185 scopus 로고    scopus 로고
    • Estimating the variance in nonparametric regression - What is a reasonable choice?
    • Dette H, Munk A and Wagner T 1998 Estimating the variance in nonparametric regression - what is a reasonable choice? J. R. Statist. Soc. B 60 751-64
    • (1998) J. R. Statist. Soc. B , vol.60 , pp. 751-764
    • Dette, H.1    Munk, A.2    Wagner, T.3
  • 6
    • 36149030945 scopus 로고
    • Convergence rates for Tikhonov regularization of nonlinear ill-posed problems
    • Engl H W, Kunisch K and Neubauer A 1989 Convergence rates for Tikhonov regularization of nonlinear ill-posed problems Inverse Problems 5 523-40
    • (1989) Inverse Problems , vol.5 , pp. 523-540
    • Engl, H.W.1    Kunisch, K.2    Neubauer, A.3
  • 9
    • 84950423285 scopus 로고
    • Design-adaptive nonparametric regression
    • Fan J 1992 Design-adaptive nonparametric regression J. Am. Stat. Assoc. 87 998-1004
    • (1992) J. Am. Stat. Assoc. , vol.87 , pp. 998-1004
    • Fan, J.1
  • 10
    • 3042869574 scopus 로고
    • Local linear regression smoothers and their minimax efficiencies
    • Fan J 1993 Local linear regression smoothers and their minimax efficiencies Ann. Statist. 21 196-216
    • (1993) Ann. Statist. , vol.21 , pp. 196-216
    • Fan, J.1
  • 12
    • 0000871211 scopus 로고    scopus 로고
    • Efficient estimation of conditional variance functions in stochastic regression
    • Fan J and Yao Q 1998 Efficient estimation of conditional variance functions in stochastic regression Biometrika 85 645-60
    • (1998) Biometrika , vol.85 , pp. 645-660
    • Fan, J.1    Yao, Q.2
  • 13
    • 0000035920 scopus 로고
    • On variance estimation in nonparametric regression
    • Hall P and Marron J S 1990 On variance estimation in nonparametric regression Biometrika 77 415-9
    • (1990) Biometrika , vol.77 , pp. 415-419
    • Hall, P.1    Marron, J.S.2
  • 14
    • 0000402476 scopus 로고
    • Optimal bandwidth selection in nonparametric regression function estimation
    • Härdle W and Marron J S 1985 Optimal bandwidth selection in nonparametric regression function estimation Ann. Statist. 13 1465-81
    • (1985) Ann. Statist. , vol.13 , pp. 1465-1481
    • Härdle, W.1    Marron, J.S.2
  • 16
    • 0004893513 scopus 로고    scopus 로고
    • Convergence rates of a regularized Newton method in sound-hard inverse scattering
    • Hohage T 1998 Convergence rates of a regularized Newton method in sound-hard inverse scattering SIAM J. Numer. Anal. 36 125-42
    • (1998) SIAM J. Numer. Anal. , vol.36 , pp. 125-142
    • Hohage, T.1
  • 18
    • 0001050272 scopus 로고    scopus 로고
    • A brief survey of bandwidth selection for density estimation
    • Jones M C, Marron J S and Sheather S J 1996 A brief survey of bandwidth selection for density estimation J. Am. Stat. Assoc. 91 401-7
    • (1996) J. Am. Stat. Assoc. , vol.91 , pp. 401-407
    • Jones, M.C.1    Marron, J.S.2    Sheather, S.J.3
  • 20
    • 12244252809 scopus 로고    scopus 로고
    • Universal consistency of local polynomial kernel regression estimates
    • Kohler M 2002 Universal consistency of local polynomial kernel regression estimates Ann. Inst. Stat. Math. 54 879-99
    • (2002) Ann. Inst. Stat. Math. , vol.54 , pp. 879-899
    • Kohler, M.1
  • 21
    • 0033438066 scopus 로고    scopus 로고
    • Bandwidth selection: Classical or plug-in?
    • Loader C R 1999 Bandwidth selection: classical or plug-in? Ann. Stat. 27 415-38
    • (1999) Ann. Stat. , vol.27 , pp. 415-438
    • Loader, C.R.1
  • 22
    • 21344495243 scopus 로고
    • Asymptotic optimality of generalized cross-validation for choosing the regularization parameter
    • Lucas M A 1993 Asymptotic optimality of generalized cross-validation for choosing the regularization parameter Numer. Math. 66 41-6
    • (1993) Numer. Math. , vol.66 , pp. 41-46
    • Lucas, M.A.1
  • 23
    • 0030269038 scopus 로고    scopus 로고
    • Statistical inverse estimation in Hilbert scales
    • Mair B A and Ruymgaart F 1996 Statistical inverse estimation in Hilbert scales SIAM J. Appl. Math. 56 1424-44
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1424-1444
    • Mair, B.A.1    Ruymgaart, F.2
  • 24
    • 0001202058 scopus 로고    scopus 로고
    • Multivariate local polynomial regression for time series: Uniform strong consistency and rates
    • Masry E 1996 Multivariate local polynomial regression for time series: uniform strong consistency and rates J. Time Series Anal. 17 571-99
    • (1996) J. Time Series Anal. , vol.17 , pp. 571-599
    • Masry, E.1
  • 25
    • 0035995089 scopus 로고    scopus 로고
    • Testing the goodness of fit of parametric regression models with random Toeplitz forms
    • Munk A 2002 Testing the goodness of fit of parametric regression models with random Toeplitz forms Scand. J. Stat. 29 501-35
    • (2002) Scand. J. Stat. , vol.29 , pp. 501-535
    • Munk, A.1
  • 26
    • 10844250596 scopus 로고    scopus 로고
    • On difference-based variance estimation in nonparametric regression when the covariate is high dimensional
    • to appear
    • Munk A, Bissantz N, Wagner T and Freitag G On difference-based variance estimation in nonparametric regression when the covariate is high dimensional J. R. Stat. Soc. (to appear)
    • J. R. Stat. Soc.
    • Munk, A.1    Bissantz, N.2    Wagner, T.3    Freitag, G.4
  • 27
    • 0000881596 scopus 로고
    • Fully data-driven nonparametric variance estimators
    • Neumann M H 1994 Fully data-driven nonparametric variance estimators Statistics 25 189-212
    • (1994) Statistics , vol.25 , pp. 189-212
    • Neumann, M.H.1
  • 28
    • 0000823716 scopus 로고
    • Convergence rates for regularized solutions of integral equations from discrete noisy data
    • Nychka D W and Cox D 1989 Convergence rates for regularized solutions of integral equations from discrete noisy data Ann. Statist. 17 556-72
    • (1989) Ann. Statist. , vol.17 , pp. 556-572
    • Nychka, D.W.1    Cox, D.2
  • 29
    • 0019622303 scopus 로고
    • An inverse problem for the steady state diffusion equation
    • Richter G R 1981 An inverse problem for the steady state diffusion equation SIAM J. Appl. Math. 4 210-21
    • (1981) SIAM J. Appl. Math. , vol.4 , pp. 210-221
    • Richter, G.R.1
  • 30
    • 84947934780 scopus 로고
    • An effective bandwidth selector for local least squares regression
    • Ruppert D, Sheather S J and Wand M P 1995 An effective bandwidth selector for local least squares regression J. Am. Statist. Assoc. 90 1257-70
    • (1995) J. Am. Statist. Assoc. , vol.90 , pp. 1257-1270
    • Ruppert, D.1    Sheather, S.J.2    Wand, M.P.3
  • 31
    • 21844518517 scopus 로고
    • Multivariate locally weighted least squares regression
    • Ruppert D and Wand M P 1994 Multivariate locally weighted least squares regression Ann. Statist. 22 1346-70
    • (1994) Ann. Statist. , vol.22 , pp. 1346-1370
    • Ruppert, D.1    Wand, M.P.2
  • 33
    • 0026172482 scopus 로고
    • An extension of Backus-Gilbert theory to nonlinear inverse problems
    • Snieder R 1991 An extension of Backus-Gilbert theory to nonlinear inverse problems Inverse Problems 7 409-33
    • (1991) Inverse Problems , vol.7 , pp. 409-433
    • Snieder, R.1
  • 34
    • 0040235973 scopus 로고
    • Convergence characteristics of method of regularization estimators for nonlinear operator equations
    • O'Sullivan F 1990 Convergence characteristics of method of regularization estimators for nonlinear operator equations SIAM J. Num. Anal. 27 1635-49
    • (1990) SIAM J. Num. Anal. , vol.27 , pp. 1635-1649
    • O'Sullivan, F.1
  • 36
    • 84963160122 scopus 로고
    • Error analyses for general multivariate kernel estimators
    • Wand M P 1992 Error analyses for general multivariate kernel estimators J. Nonp. Statist. 2 1-15
    • (1992) J. Nonp. Statist. , vol.2 , pp. 1-15
    • Wand, M.P.1
  • 38
    • 0027695591 scopus 로고
    • A regularization method for nonlinear ill-posed problems
    • Weese J 1993 A regularization method for nonlinear ill-posed problems Comput. Phys. Commun. 77 429-40
    • (1993) Comput. Phys. Commun. , vol.77 , pp. 429-440
    • Weese, J.1
  • 40
    • 0036859875 scopus 로고    scopus 로고
    • Asymptotic behaviour of bandwidth selected by the cross-validation method for local polynomial fitting
    • Xia Y and Li W K 2002 Asymptotic behaviour of bandwidth selected by the cross-validation method for local polynomial fitting J. Multiv. Anal. 83 265-87
    • (2002) J. Multiv. Anal. , vol.83 , pp. 265-287
    • Xia, Y.1    Li, W.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.