메뉴 건너뛰기




Volumn 21, Issue 2, 1979, Pages 215-223

Generalized cross-validation as a method for choosing a good ridge parameter

Author keywords

Cross validation; Ridge parameter; Ridge regression

Indexed keywords


EID: 32044449925     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1979.10489751     Document Type: Article
Times cited : (3150)

References (46)
  • 1
    • 0016355478 scopus 로고
    • A new look at the statistical model identification
    • AKAIKE, H. (1974). A new look at the statistical model identification. IEEE Transaction on Automatic Control, AC- 19, 6, 716-730.
    • (1974) IEEE Transaction on Automatic Control, AC , vol.19 , Issue.6 , pp. 716-730
    • Akaike, H.1
  • 2
    • 84952081992 scopus 로고
    • Mean square error of prediction as a criterion for selecting variables
    • ALLEN, D. M. (1971). Mean square error of prediction as a criterion for selecting variables. Technometrics, 13, 469-475.
    • (1971) Technometrics , vol.13 , pp. 469-475
    • Allen, D.M.1
  • 3
    • 0016029778 scopus 로고
    • The relationship between variable selection and data augmentation and a method for prediction
    • ALLEN, D. M. (1974). The relationship between variable selection and data augmentation and a method for prediction. Technometrics, 16, 125-127.
    • (1974) Technometrics , vol.16 , pp. 125-127
    • Allen, D.M.1
  • 4
    • 0001061872 scopus 로고
    • Numerical differentiation procedures for non-exact data
    • ANDERSSEN, B. and BLOOMFIELD, P. (1974). Numerical differentiation procedures for non-exact data. Numer. Math., 22. 157-182.
    • (1974) Numer. Math , vol.22 , pp. 157-182
    • Anderssen, B.1    Bloomfield, P.2
  • 5
    • 0002431823 scopus 로고
    • A time series approach to numerical differentiation
    • ANDERSSEN, R. S. and BLOOMFIELD, P. (1974). A time series approach to numerical differentiation. Technometrics, 16, 69-75.
    • (1974) Technometrics , vol.16 , pp. 69-75
    • Anderssen, R.S.1    Bloomfield, P.2
  • 6
    • 50549200054 scopus 로고
    • BAKER, C. T. H., FOX, L., MAYERS, D. F., and WRIGHT, K. (1964). Numerical solution of Fredholm integral equations of the first kind. Comp. J., 7, 141-148.
    • (1964) Comp. J , vol.7 , pp. 141-148
    • Baker, C.1    Fox, L.2    Mayers, D.F.3    Wright, K.4
  • 8
    • 0016963035 scopus 로고
    • Minimax estimation of a multivariate normal mean under arbitrary quadratric loss
    • BERGER, J. (1976). Minimax estimation of a multivariate normal mean under arbitrary quadratric loss. J. Multivariate Analysis, 6, 256-264.
    • (1976) J. Multivariate Analysis , vol.6 , pp. 256-264
    • Berger, J.1
  • 9
    • 34250263445 scopus 로고
    • Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
    • CRAVEN, P. and WAHBA, G. (1979). Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math., 31, 377-403.
    • (1979) Numer. Math , vol.31 , pp. 377-403
    • Craven, P.1    Wahba, G.2
  • 10
    • 84952101859 scopus 로고
    • Alternatives to least squares in multiple regression, In Multivariate Statistical Conference
    • Dalhousie University, Halifax, March 23-25, 1972, ed. by D. G. Kabe and R. P. Gupta
    • DEMPSTER, A. P. (1973). Alternatives to least squares in multiple regression, In Multivariate Statistical Conference, Proceedings of the Research Seminar at Dalhousie University, Halifax, March 23-25, 1972, ed. by D. G. Kabe and R. P. Gupta.
    • (1973) Proceedings of the Research Seminar
    • Dempster, A.P.1
  • 11
    • 0001838289 scopus 로고
    • A simulation study of alternatives to ordinary least squares
    • DEMPSTER, A. P., SCHATZOFF, M., and WERMUTH, N. (1975). A simulation study of alternatives to ordinary least squares. J. Amer. Statist. Assoc., 70, 77-106.
    • (1975) J. Amer. Statist. Assoc , vol.70 , pp. 77-106
    • Dempster, A.P.1    Schatzoff, M.2    Wermuth, N.3
  • 12
    • 0000379612 scopus 로고
    • The minimum mean square error linear estimator and ridge regression
    • FAREBROTHER, R. W. (1975). The minimum mean square error linear estimator and ridge regression. Technometrics, 17, 127-128.
    • (1975) Technometrics , vol.17 , pp. 127-128
    • Farebrother, R.W.1
  • 13
    • 84950645271 scopus 로고
    • The predictive sample reuse method with applications
    • GEISSER, S. (1975). The predictive sample reuse method with applications. J. Amer. Statist. Assoc., 70, 320-328.
    • (1975) J. Amer. Statist. Assoc , vol.70 , pp. 320-328
    • Geisser, S.1
  • 15
    • 0001145061 scopus 로고
    • Ridge type estimators for regression analysis
    • B
    • GOLDSTEIN, M., and SMITH, A. F. M. (1974). Ridge type estimators for regression analysis. J. Roy. Statist. Soc., Ser. B, 36, 284-291.
    • (1974) J. Roy. Statist. Soc., Ser , vol.36 , pp. 284-291
    • Goldstein, M.1    Smith, A.2
  • 16
    • 33747738463 scopus 로고
    • Singular value decomposition and least squares solutions
    • GOLUB, G., and REINSCH, C. (1970). Singular value decomposition and least squares solutions. Numer. Math., 14, 403-420.
    • (1970) Numer. Math , vol.14 , pp. 403-420
    • Golub, G.1    Reinsch, C.2
  • 17
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • GOLUB, G. H. (1973). Some modified matrix eigenvalue problems. SIAM Review, 15, 318-334.
    • (1973) SIAM Review , vol.15 , pp. 318-334
    • Golub, G.H.1
  • 19
    • 0015127540 scopus 로고
    • A numerical method for solving Fredholm integral equations of the first kind using singular values
    • HANSON, R. J. (1971). A numerical method for solving Fredholm integral equations of the first kind using singular values. SIAM J. Num. Anal., 8, 616-622.
    • (1971) SIAM J. Num. Anal , vol.8 , pp. 616-622
    • Hanson, R.J.1
  • 20
    • 0016540049 scopus 로고
    • An explicit solution for generalized ridge regression
    • HEMMERLE, W. J. (1975). An explicit solution for generalized ridge regression. Technometrics, 17, 309-313.
    • (1975) Technometrics , vol.17 , pp. 309-313
    • Hemmerle, W.J.1
  • 21
    • 0016943084 scopus 로고
    • On the equivalence of regularization and certain reproducing kernel Hilbert space approaches for solving first kind problems
    • HILGERS, J. W. (1976). On the equivalence of regularization and certain reproducing kernel Hilbert space approaches for solving first kind problems. SIAM J. Num. Anal., 15, 172- 184.
    • (1976) SIAM J. Num. Anal , vol.15
    • Hilgers, J.W.1
  • 22
    • 84950232981 scopus 로고
    • HOERL, A. E., and KENNARD, R. W. (1976). Ridge regression: iterative estimation of the biasing parameter. Comm, in Statist., A5, 77-88.
    • (1976) Comm, in Statist , vol.A5 , pp. 77-88
    • Hoerl, A.E.1    Kennard, R.W.2
  • 25
    • 0041750328 scopus 로고
    • Technical Report No. 58, Stanford University, Department of Statistics, Stanford, CA
    • HUDSON, H. M. (1974). Empirical Bayes estimation. Technical Report No. 58, Stanford University, Department of Statistics, Stanford, CA.
    • (1974) Empirical Bayes Estimation
    • Hudson, H.M.1
  • 26
    • 84948495975 scopus 로고
    • A simulation study of ridge and other regression estimators
    • LAWLESS, J. F. and WANG, P. (1976). A simulation study of ridge and other regression estimators. Comm, in Statist., A5, 307-324.
    • (1976) Comm, in Statist , vol.A5 , pp. 307-324
    • Lawless, J.F.1    Wang, P.2
  • 27
    • 0003232065 scopus 로고
    • Bayes estimate for the linear model (With discussion)
    • B
    • LINDLEY, D. V., and SMITH, A. F. M. (1972). Bayes estimate for the linear model (with discussion), part 1.7. Roy. Statist. Soc., B, 34, 1-41.
    • (1972) Roy. Statist. Soc. , vol.34 , pp. 1-41
    • Lindley, D.V.1    Smith, A.2
  • 28
    • 84915425007 scopus 로고
    • Some comments on Cp
    • MALLOWS, C. L. (1973). Some comments on Cp. Technometrics, 15, 661-675.
    • (1973) Technometrics , vol.15 , pp. 661-675
    • Mallows, C.L.1
  • 29
    • 84944477553 scopus 로고
    • Generalized inverses, ridge regression, biased linear estimation and nonlinear estimation
    • MARQUARDT, D. W. (1970). Generalized inverses, ridge regression, biased linear estimation and nonlinear estimation. Technometrics, 12, 591-64.
    • (1970) Technometrics , vol.12 , pp. 591-664
    • Marquardt, D.W.1
  • 31
    • 84950610670 scopus 로고
    • A Monte Carlo evaluation of some ridge-type estimators
    • MCDONALD, G. and GALARNEAU, D. (1975). A Monte Carlo evaluation of some ridge-type estimators. J. Amer. Statist. Assoc., 70, 407-416.
    • (1975) J. Amer. Statist. Assoc , vol.70 , pp. 407-416
    • McDonald, G.1    Galarneau, D.2
  • 32
    • 0016574934 scopus 로고
    • Ridge Analysis following a preliminary test of the shrunken hypothesis
    • OBENCHAIN, R. L. (1975). Ridge Analysis following a preliminary test of the shrunken hypothesis. Technometrics, 17, 431-446.
    • (1975) Technometrics , vol.17 , pp. 431-446
    • Obenchain, R.L.1
  • 35
    • 84946273625 scopus 로고
    • Choosing shrinkage estimators for regression problems
    • ROLPH, J. E. (1976). Choosing shrinkage estimators for regression problems. Comm, in Statist., A5, 789-802.
    • (1976) Comm, in Statist , vol.A5 , pp. 789-802
    • Rolph, J.E.1
  • 36
    • 0000629975 scopus 로고
    • Cross-validatory choice and assessment of statistical prediction
    • B
    • STONE, M. (1974). Cross-validatory choice and assessment of statistical prediction. J. Roy. Statist. Soc., B, 36, 111-147.
    • (1974) J. Roy. Statist. Soc. , vol.36 , pp. 111-147
    • Stone, M.1
  • 37
    • 0000859675 scopus 로고
    • An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion
    • B
    • STONE, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike's criterion. J. Roy. Statist. Soc., B., 39, 44-47.
    • (1977) J. Roy. Statist. Soc. , vol.39 , pp. 44-47
    • Stone, M.1
  • 38
    • 0011556857 scopus 로고
    • Good ridge estimators based on prior information
    • SWINDEL, B. F. (1976). Good ridge estimators based on prior information. Comm, in Statist., A5, 985-997.
    • (1976) Comm, in Statist , vol.A5 , pp. 985-997
    • Swindel, B.F.1
  • 39
    • 0006345655 scopus 로고
    • Ridge regression, minimax estimation, and empirical Bayes methods
    • Stanford University, Tech. Report No. 28
    • THISTED, R. A. (1976). Ridge regression, minimax estimation, and empirical Bayes methods. Division of Biostatistics, Stanford University, Tech. Report No. 28.
    • (1976) Division of Biostatistics
    • Thisted, R.A.1
  • 40
    • 0000296726 scopus 로고
    • On the numerical solution of ill- conditioned linear systems with applications to ill posed problems
    • VARAH, J. M. (1973). On the numerical solution of ill- conditioned linear systems with applications to ill posed problems. SIAM J. Num. Anal., 10, 257-267.
    • (1973) SIAM J. Num. Anal , vol.10 , pp. 257-267
    • Varah, J.M.1
  • 41
    • 3643091596 scopus 로고
    • On the distribution of some statistics useful in the analysis of jointly stationary time series
    • WAHBA, G. (1968). On the distribution of some statistics useful in the analysis of jointly stationary time series. Ann. Math. Statist., 39, 1849-1862.
    • (1968) Ann. Math. Statist , vol.39 , pp. 1849-1862
    • Wahba, G.1
  • 42
    • 0002328596 scopus 로고
    • A survey of some smoothing problems and the method of generalized cross-validation for solving them
    • held at Dayton, Ohio, June 14-17, 1976, ed. by P. R. Krishnaiah
    • WAHBA, G. (1976). A survey of some smoothing problems and the method of generalized cross-validation for solving them. In Proceedings of the Conference on the Applications of Statistics, held at Dayton, Ohio, June 14-17, 1976, ed. by P. R. Krishnaiah.
    • (1976) In Proceedings of the Conference on the Applications of Statistics
    • Wahba, G.1
  • 43
    • 0041140911 scopus 로고
    • Optimal smoothing of density estimates
    • by J. Van Ry- zin. New York: Academic Press
    • WAHBA, G. (1976). Optimal smoothing of density estimates. Classification and Clustering, pp. 423-458, ed. by J. Van Ry- zin. New York: Academic Press.
    • (1976) Classification and Clustering , pp. 423-458
    • Wahba, G.1
  • 44
    • 0000544453 scopus 로고
    • The approximate solution of linear operator equations when the data are noisy
    • WAHBA, G. (1977). The approximate solution of linear operator equations when the data are noisy. SIAM J. Num. Anal, 14, 651-667.
    • (1977) SIAM J. Num. Anal , vol.14 , pp. 651-667
    • Wahba, G.1
  • 45
    • 0000620787 scopus 로고
    • Periodic splines for spectral density estimation: The use of cross-validation for determining the correct degree of smoothing
    • WAHBA, G., and WOLD, S. (1975). Periodic splines for spectral density estimation: the use of cross-validation for determining the correct degree of smoothing. Comm, in Statist., 4, 125-141.
    • (1975) Comm, in Statist , vol.4 , pp. 125-141
    • Wahba, G.1    Wold, S.2
  • 46
    • 0002617598 scopus 로고
    • A completely automatic French curve: Fitting spline functions by cross-validation
    • WAHBA, G., and WOLD, S. (1975). A completely automatic French curve: fitting spline functions by cross-validation. Comm, in Statist., 4, 1-17.
    • (1975) Comm, in Statist. , vol.4 , pp. 1-17
    • Wahba, G.1    Wold, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.