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Volumn 235, Issue 1, 2010, Pages 102-107

Efficient algorithms for robust generalized cross-validation spline smoothing

Author keywords

Cholesky decomposition; Generalized cross validation; Smoothing matrix; Smoothing parameter; Spline; Trace

Indexed keywords

CHOLESKY DECOMPOSITION; COMPUTATIONAL EFFORT; EFFICIENT ALGORITHM; FUNCTIONALS; GENERALIZED CROSS VALIDATION; MATRIX; O ALGORITHM; PARAMETER SELECTION; SAMPLE SIZES; SMOOTHING PARAMETER;

EID: 77955430776     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.05.016     Document Type: Article
Times cited : (27)

References (28)
  • 3
    • 34250263445 scopus 로고
    • Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
    • P. Craven, and G. Wahba Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation Numer. Math. 31 1979 377 403
    • (1979) Numer. Math. , vol.31 , pp. 377-403
    • Craven, P.1    Wahba, G.2
  • 4
    • 0000872265 scopus 로고
    • Making robust the cross-validatory choice of smoothing parameter in spline smoothing regression
    • T. Robinson, and R. Moyeed Making robust the cross-validatory choice of smoothing parameter in spline smoothing regression Comm. Statist. Theory Methods 18 1989 523 539
    • (1989) Comm. Statist. Theory Methods , vol.18 , pp. 523-539
    • Robinson, T.1    Moyeed, R.2
  • 5
    • 33749009570 scopus 로고    scopus 로고
    • Robust generalized cross-validation for choosing the regularization parameter
    • M.A. Lukas Robust generalized cross-validation for choosing the regularization parameter Inverse Problems 22 2006 1883 1902
    • (2006) Inverse Problems , vol.22 , pp. 1883-1902
    • Lukas, M.A.1
  • 6
    • 44449133545 scopus 로고    scopus 로고
    • Strong robust generalized cross-validation for choosing the regularization parameter
    • M.A. Lukas Strong robust generalized cross-validation for choosing the regularization parameter Inverse Problems 24 2008 034006
    • (2008) Inverse Problems , vol.24 , pp. 034006
    • Lukas, M.A.1
  • 7
    • 1842665178 scopus 로고    scopus 로고
    • Confidence intervals for nonparametric curve estimates: Toward more uniform pointwise coverage
    • D.J. Cummins, T.G. Filloon, and D. Nychka Confidence intervals for nonparametric curve estimates: toward more uniform pointwise coverage J. Amer. Statist. Assoc. 96 2001 233 246
    • (2001) J. Amer. Statist. Assoc. , vol.96 , pp. 233-246
    • Cummins, D.J.1    Filloon, T.G.2    Nychka, D.3
  • 8
    • 2442486641 scopus 로고    scopus 로고
    • Smoothing spline Gaussian regression: More scalable computation via efficient approximation
    • Y.-J. Kim, and C. Gu Smoothing spline Gaussian regression: more scalable computation via efficient approximation J. Roy. Statist. Soc. Ser. B 66 2004 337 356
    • (2004) J. Roy. Statist. Soc. Ser. B , vol.66 , pp. 337-356
    • Kim, Y.-J.1    Gu, C.2
  • 10
    • 34250516079 scopus 로고
    • Smoothing by spline functions
    • C.H. Reinsch Smoothing by spline functions Numer. Math. 10 1967 177 183
    • (1967) Numer. Math. , vol.10 , pp. 177-183
    • Reinsch, C.H.1
  • 11
    • 11644266571 scopus 로고
    • Smoothing by spline functions II
    • C.H. Reinsch Smoothing by spline functions II Numer. Math. 16 1971 451 454
    • (1971) Numer. Math. , vol.16 , pp. 451-454
    • Reinsch, C.H.1
  • 12
    • 0002970891 scopus 로고
    • Smoothing noisy data with spline functions
    • M.F. Hutchinson, and F.R. de Hoog Smoothing noisy data with spline functions Numer. Math. 47 1985 99 106
    • (1985) Numer. Math. , vol.47 , pp. 99-106
    • Hutchinson, M.F.1    De Hoog, F.R.2
  • 13
    • 0000939344 scopus 로고
    • Bayesian "confidence intervals" for the cross-validated smoothing spline
    • G. Wahba Bayesian "confidence intervals" for the cross-validated smoothing spline J. Roy. Statist. Soc. Ser. B 45 1983 133 150
    • (1983) J. Roy. Statist. Soc. Ser. B , vol.45 , pp. 133-150
    • Wahba, G.1
  • 14
    • 0037877555 scopus 로고
    • Computation of smoothing and interpolating natural splines via local bases
    • T. Lyche, and L.L. Schumaker Computation of smoothing and interpolating natural splines via local bases SIAM J. Numer. Anal. 10 1973 1027 1038
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 1027-1038
    • Lyche, T.1    Schumaker, L.L.2
  • 15
    • 0009034842 scopus 로고
    • Discussion of "some aspects of the spline smoothing approach to non-parametric regression curve fitting" by B.W. Silverman
    • F. O'Sullivan Discussion of "some aspects of the spline smoothing approach to non-parametric regression curve fitting" by B.W. Silverman J. Roy. Statist. Soc. Ser. B 47 1985 39 40
    • (1985) J. Roy. Statist. Soc. Ser. B , vol.47 , pp. 39-40
    • O'Sullivan, F.1
  • 17
    • 0042560714 scopus 로고
    • An efficient method for calculating smoothing splines using orthogonal transformations
    • F.R. de Hoog, and M.F. Hutchinson An efficient method for calculating smoothing splines using orthogonal transformations Numer. Math. 50 1987 311 319
    • (1987) Numer. Math. , vol.50 , pp. 311-319
    • De Hoog, F.R.1    Hutchinson, M.F.2
  • 18
    • 0000463893 scopus 로고
    • An algorithm for the regularization of ill-conditioned, banded least squares problems
    • L. Eldn An algorithm for the regularization of ill-conditioned, banded least squares problems SIAM J. Sci. Stat. Comput. 5 1984 237 254
    • (1984) SIAM J. Sci. Stat. Comput. , vol.5 , pp. 237-254
    • Eldn, L.1
  • 20
    • 0000935894 scopus 로고
    • Spline smoothing and optimal rates of convergence in nonparametric regression models
    • P. Speckman Spline smoothing and optimal rates of convergence in nonparametric regression models Ann. Statist. 13 1985 970 983
    • (1985) Ann. Statist. , vol.13 , pp. 970-983
    • Speckman, P.1
  • 21
    • 84950454897 scopus 로고
    • A fast and efficient cross-validation method for smoothing parameter choice in spline regression
    • B.W. Silverman A fast and efficient cross-validation method for smoothing parameter choice in spline regression J. Amer. Statist. Assoc. 79 1984 584 589
    • (1984) J. Amer. Statist. Assoc. , vol.79 , pp. 584-589
    • Silverman, B.W.1
  • 22
    • 0002882706 scopus 로고
    • A fast "monte-Carlo cross-validation" procedure for large least squares problems with noisy data
    • D.A. Girard A fast "Monte-Carlo cross-validation" procedure for large least squares problems with noisy data Numer. Math. 56 1989 1 23
    • (1989) Numer. Math. , vol.56 , pp. 1-23
    • Girard, D.A.1
  • 23
    • 0000462797 scopus 로고
    • A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
    • M.F. Hutchinson A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines Comm. Statist. Simulation Comput. 18 1989 1059 1076
    • (1989) Comm. Statist. Simulation Comput. , vol.18 , pp. 1059-1076
    • Hutchinson, M.F.1
  • 24
    • 0002939160 scopus 로고
    • A comparison of the Reinsch and Speckman splines
    • C.K. Carter, G.K. Eagleson, and B.W. Silverman A comparison of the Reinsch and Speckman splines Biometrika 79 1992 81 91
    • (1992) Biometrika , vol.79 , pp. 81-91
    • Carter, C.K.1    Eagleson, G.K.2    Silverman, B.W.3
  • 25
    • 0000014224 scopus 로고
    • Linear smoothers and additive models
    • A. Buja, T. Hastie, and R. Tibshirani Linear smoothers and additive models Ann. Statist. 17 2 1989 453 555
    • (1989) Ann. Statist. , vol.17 , Issue.2 , pp. 453-555
    • Buja, A.1    Hastie, T.2    Tibshirani, R.3
  • 26
    • 0002014881 scopus 로고
    • A general method for the construction of interpolating or smoothing spline-functions
    • P.M. Anselone, and P.J. Laurent A general method for the construction of interpolating or smoothing spline-functions Numer. Math. 12 1968 66 82
    • (1968) Numer. Math. , vol.12 , pp. 66-82
    • Anselone, P.M.1    Laurent, P.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.