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Volumn 32, Issue 4, 2004, Pages 1723-1743

Statistical properties of the method of regularization with periodic Gaussian reproducing kernel

Author keywords

Asymptotic minimax risk; Gaussian reproducing kernel; Nonparametric estimation; Rate of convergence; Sobolev spaces; White noise model

Indexed keywords


EID: 24344444131     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000000454     Document Type: Article
Times cited : (18)

References (22)
  • 1
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • BROWN, L. D. and Low, M. G. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398.
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.D.1    Low, M.G.2
  • 2
    • 0005943602 scopus 로고    scopus 로고
    • Direct asymptotic equivalence of nonparametric regression and the infinite dimensional location problem
    • BROWN, L. D. and ZHAO, L. H. (2002). Direct asymptotic equivalence of nonparametric regression and the infinite dimensional location problem. Technical report. Available at http://ljsavage.wharton.upenn.edu/~lzhao/papers/.
    • (2002) Technical Report
    • Brown, L.D.1    Zhao, L.H.2
  • 3
    • 0002939160 scopus 로고
    • Comparison of the Reinsch and Speckman splines
    • CARTER, C. K., EAGLESON, G. K. and SILVERMAN, B. W. (1992). Comparison of the Reinsch and Speckman splines. Biometrika 79 81-91.
    • (1992) Biometrika , vol.79 , pp. 81-91
    • Carter, C.K.1    Eagleson, G.K.2    Silverman, B.W.3
  • 5
    • 0034419669 scopus 로고    scopus 로고
    • Regularization networks and support vector machines
    • EVGENIOU, T., PONTIL, M. and POGGIO, T. (2000). Regularization networks and support vector machines. Adv. Comput. Math. 13 1-50.
    • (2000) Adv. Comput. Math. , vol.13 , pp. 1-50
    • Evgeniou, T.1    Pontil, M.2    Poggio, T.3
  • 6
    • 0006801778 scopus 로고
    • Priors, stabilizers and basis functions: From regularization to radial, tensor and additive splines
    • C.B.C.I. Paper 75
    • GIOSI, F., JONES, M. and POGGIO, T. (1993). Priors, stabilizers and basis functions: From regularization to radial, tensor and additive splines. M.I.T. Artificial Intelligence Laboratory Memo 1430, C.B.C.I. Paper 75.
    • (1993) M.I.T. Artificial Intelligence Laboratory Memo , vol.1430
    • Giosi, F.1    Jones, M.2    Poggio, T.3
  • 7
    • 0043114357 scopus 로고    scopus 로고
    • Asymptotic equivalence of spectral density and regression estimation
    • Weierstrass Institute for Applied Analysis and Stochastics, Berlin
    • GOLUBEV, G. and NUSSBAUM, M. (1998). Asymptotic equivalence of spectral density and regression estimation. Technical report, Weierstrass Institute for Applied Analysis and Stochastics, Berlin.
    • (1998) Technical Report
    • Golubev, G.1    Nussbaum, M.2
  • 8
    • 24344448459 scopus 로고    scopus 로고
    • Asymptotic equivalence for nonparametric generalized linear models
    • Weierstrass Institute for Applied Analysis and Stochastics, Berlin
    • GRAMA, I. and NUSSBAUM, M. (1997). Asymptotic equivalence for nonparametric generalized linear models. Technical report, Weierstrass Institute for Applied Analysis and Stochastics, Berlin.
    • (1997) Technical Report
    • Grama, I.1    Nussbaum, M.2
  • 11
    • 0015000439 scopus 로고
    • Some results on Tchebycheffian spline functions
    • KIMELDORF, G. S. and WAHBA, G. (1971). Some results on Tchebycheffian spline functions. J. Math. Anal. Appl. 33 82-95.
    • (1971) J. Math. Anal. Appl. , vol.33 , pp. 82-95
    • Kimeldorf, G.S.1    Wahba, G.2
  • 12
    • 21844488410 scopus 로고
    • Ordered linear smoothers
    • KNEIP, A. (1994). Ordered linear smoothers. Ann. Statist. 22 835-866.
    • (1994) Ann. Statist. , vol.22 , pp. 835-866
    • Kneip, A.1
  • 13
    • 0001182369 scopus 로고
    • Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing
    • LI, K.-C. (1986). Asymptotic optimality of CL and generalized cross-validation in ridge regression with application to spline smoothing. Ann. Statist. 14 1101-1112.
    • (1986) Ann. Statist. , vol.14 , pp. 1101-1112
    • Li, K.-C.1
  • 14
    • 0001462696 scopus 로고
    • L, cross-validation and generalized cross-validation: Discrete index set
    • L, cross-validation and generalized cross-validation: Discrete index set. Ann. Statist. 15 958-975.
    • (1987) Ann. Statist. , vol.15 , pp. 958-975
    • Li, K.-C.1
  • 16
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • NUSSBAUM, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430.
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 17
    • 0000056062 scopus 로고
    • Optimal filtering of square integrable signals in Gaussian white noise
    • PINSKER, M. (1980). Optimal filtering of square integrable signals in Gaussian white noise. Problems Inform. Transmission 16 120-133.
    • (1980) Problems Inform. Transmission , vol.16 , pp. 120-133
    • Pinsker, M.1
  • 19
    • 0032098361 scopus 로고    scopus 로고
    • The connection between regularization operators and support vector kernels
    • SMOLA, A. J., SCHÖLKOPF, B. and MÜLLER, K. (1998). The connection between regularization operators and support vector kernels. Neural Networks 11 637-649.
    • (1998) Neural Networks , vol.11 , pp. 637-649
    • Smola, A.J.1    Schölkopf, B.2    Müller, K.3
  • 21
    • 0001873883 scopus 로고    scopus 로고
    • Support vector machines, reproducing kernel Hilbert spaces and randomized GACV
    • (B. Schölkopf, C. J. Burges and A. J. Smola, eds.) MIT Press, Cambridge, MA
    • WAHBA, G. (1999). Support vector machines, reproducing kernel Hilbert spaces and randomized GACV. In Advances in Kernel Methods: Support Vector Learning (B. Schölkopf, C. J. Burges and A. J. Smola, eds.) 69-88. MIT Press, Cambridge, MA.
    • (1999) Advances in Kernel Methods: Support Vector Learning , pp. 69-88
    • Wahba, G.1
  • 22
    • 0035441827 scopus 로고    scopus 로고
    • Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators
    • WILLIAMSON, R. C., SMOLA, A. J. and SCHÖLKOPF, B. (2001). Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators. IEEE Trans. Inform. Theory 47 2516-2532.
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2516-2532
    • Williamson, R.C.1    Smola, A.J.2    Schölkopf, B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.