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Volumn 9, Issue 2, 1999, Pages 475-499

Model selection for nonparametric regression

Author keywords

Adaptive estimation; Model complexity; Model selection; Nonparametric regression; Rates of convergence

Indexed keywords


EID: 0346208510     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (55)

References (39)
  • 1
    • 51249190305 scopus 로고
    • Statistical prediction identification
    • Akaike, H. (1970). Statistical prediction identification. Ann. Inst. Statist. Math. 22, 203-217.
    • (1970) Ann. Inst. Statist. Math. , vol.22 , pp. 203-217
    • Akaike, H.1
  • 2
    • 0000501656 scopus 로고
    • Information theory and an extension of the maximum likelihood principle
    • Edited by B. N. Petrov and F. Csaki, Akademia Kiado, Budapest
    • Akaike, H. (1972). Information theory and an extension of the maximum likelihood principle. In Proc. 2nd Int. Symp. Info. Theory (Edited by B. N. Petrov and F. Csaki), 267-281. Akademia Kiado, Budapest.
    • (1972) Proc. 2nd Int. Symp. Info. Theory , pp. 267-281
    • Akaike, H.1
  • 3
    • 0003757634 scopus 로고
    • Ph.D. dissertation, Department of Electrical Engineering, Stanford University
    • Barron, A. R. (1985). Logistically smooth density estimation. Ph.D. dissertation, Department of Electrical Engineering, Stanford University.
    • (1985) Logistically Smooth Density Estimation
    • Barron, A.R.1
  • 4
    • 0027599793 scopus 로고
    • Universal approximation bounds for superposition of a sigmoidal function
    • Barron, A. R. (1993). Universal approximation bounds for superposition of a sigmoidal function. IEEE Trans. Inform. Theory 39, 930-945.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 5
    • 0001325515 scopus 로고
    • Approximation and estimation bounds for artificial neural networks
    • Barron, A. R. (1994). Approximation and estimation bounds for artificial neural networks. Machine Learning 14, 115-133.
    • (1994) Machine Learning , vol.14 , pp. 115-133
    • Barron, A.R.1
  • 6
    • 0000404653 scopus 로고
    • Approximation of density functions by sequences of exponential families
    • Barron, A. R. and Sheu, C.-H. (1991). Approximation of density functions by sequences of exponential families. Ann. Statist. 19, 1347-1369.
    • (1991) Ann. Statist. , vol.19 , pp. 1347-1369
    • Barron, A.R.1    Sheu, C.-H.2
  • 7
    • 0026190366 scopus 로고
    • Minimum complexity density estimation
    • Barron, A. R. and Cover, T. M. (1991). Minimum complexity density estimation. IEEE Trans. Inform. Theory 37, 1034-1054.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 1034-1054
    • Barron, A.R.1    Cover, T.M.2
  • 10
    • 0030327799 scopus 로고    scopus 로고
    • A constrained risk inequality with applications to non-parametric functional estimation
    • Brown, L. D. and Low, M. G. (1996). A constrained risk inequality with applications to non-parametric functional estimation. Ann. Statist. 24, 2524-2535.
    • (1996) Ann. Statist. , vol.24 , pp. 2524-2535
    • Brown, L.D.1    Low, M.G.2
  • 11
    • 38249019766 scopus 로고
    • Estimation of generalized additive models
    • Burman, P. (1990). Estimation of generalized additive models. J. Multiariate Anal. 32, 230-255.
    • (1990) J. Multiariate Anal. , vol.32 , pp. 230-255
    • Burman, P.1
  • 12
    • 0000317016 scopus 로고
    • Interaction spline models and their convergence rates
    • Chen, Z. (1991). Interaction spline models and their convergence rates. Ann. Statist. 19, 1855-1868.
    • (1991) Ann. Statist. , vol.19 , pp. 1855-1868
    • Chen, Z.1
  • 14
    • 0032334093 scopus 로고    scopus 로고
    • Minimax estimation via Wavelet Shrinkage
    • Donoho, D. and Johnstone, I. (1998). Minimax estimation via Wavelet Shrinkage. Ann. Statist. 26, 879-921.
    • (1998) Ann. Statist. , vol.26 , pp. 879-921
    • Donoho, D.1    Johnstone, I.2
  • 16
    • 0012722713 scopus 로고
    • Nonparametric estimation of a density of unknown smoothness
    • Efroimovich, S. Yu. (1985). Nonparametric estimation of a density of unknown smoothness. Theory Probab. Appl. 30, 557-568.
    • (1985) Theory Probab. Appl. , vol.30 , pp. 557-568
    • Efroimovich, S.Yu.1
  • 17
    • 0002409695 scopus 로고
    • A self-educating nonparametric filtration algorithm
    • Efroimovich, S. Yu. and Pinsker, M. S. (1984). A self-educating nonparametric filtration algorithm. Automat. Remote Control 45, 58-65.
    • (1984) Automat. Remote Control , vol.45 , pp. 58-65
    • Efroimovich, S.Yu.1    Pinsker, M.S.2
  • 18
    • 0016486577 scopus 로고
    • Universal codeword sets and representation of integers
    • Elias, P. (1975). Universal codeword sets and representation of integers. IEEE Trans. Inform. Theory 21, 194-203.
    • (1975) IEEE Trans. Inform. Theory , vol.21 , pp. 194-203
    • Elias, P.1
  • 19
    • 0000666757 scopus 로고
    • On stochastic complexity and nonparametric density estimation
    • Hall, P. and Hannan, E. J. (1988). On stochastic complexity and nonparametric density estimation. Biometrika 75, 705-714.
    • (1988) Biometrika , vol.75 , pp. 705-714
    • Hall, P.1    Hannan, E.J.2
  • 20
    • 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, 1465-1481.
    • (1985) Ann. Statist. , vol.13 , pp. 1465-1481
    • Härdle, W.1    Marron, J.S.2
  • 21
    • 0001066342 scopus 로고
    • Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates
    • Lepskii, O. V. (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
    • Lepskii, O.V.1
  • 22
    • 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
  • 23
    • 84956083720 scopus 로고
    • Metric entropy and approximation
    • Lorentz, G. G. (1966). Metric entropy and approximation. Bull. Amer. Math. Soc. 72, 903-937.
    • (1966) Bull. Amer. Math. Soc. , vol.72 , pp. 903-937
    • Lorentz, G.G.1
  • 26
    • 0001289292 scopus 로고
    • p-test for the orthogonal series estimation of regression
    • p-test for the orthogonal series estimation of regression. Theory Probab. Appl. 35, 293-306.
    • (1990) Theory Probab. Appl. , vol.35 , pp. 293-306
    • Polyak, B.T.1    Tsybakov, A.B.2
  • 27
    • 0001098776 scopus 로고
    • A universal prior for integers and estimation by minimum description length
    • Rissanen, J. (1983). A universal prior for integers and estimation by minimum description length. Ann. Statist. 11, 416-431.
    • (1983) Ann. Statist. , vol.11 , pp. 416-431
    • Rissanen, J.1
  • 28
    • 0021466584 scopus 로고
    • Universal coding, information, prediction, and estimation
    • Rissanen, J. (1984). Universal coding, information, prediction, and estimation. IEEE Trans. Inform. Theory 30, 629-636.
    • (1984) IEEE Trans. Inform. Theory , vol.30 , pp. 629-636
    • Rissanen, J.1
  • 29
  • 30
    • 0012856304 scopus 로고
    • Asymptotic mean efficiency of a selection of regression variables
    • Shibata, R. (1983). Asymptotic mean efficiency of a selection of regression variables. Ann. Inst. Statist. Math. 35, 415-423.
    • (1983) Ann. Inst. Statist. Math. , vol.35 , pp. 415-423
    • Shibata, R.1
  • 32
    • 0000388992 scopus 로고
    • Consistent nonparametric regression
    • Stone, C. J. (1977). Consistent nonparametric regression. Ann. Statist. 5, 595-620.
    • (1977) Ann. Statist. , vol.5 , pp. 595-620
    • Stone, C.J.1
  • 33
    • 0001227575 scopus 로고
    • Additive regression and other nonparametric models
    • Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist. 13, 689-705.
    • (1985) Ann. Statist. , vol.13 , pp. 689-705
    • Stone, C.J.1
  • 34
    • 0346862811 scopus 로고
    • The use of polynomial splines and their tensor products in multivariate function estimation
    • Stone, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation. Ann. Statist. 22, 118-184.
    • (1994) Ann. Statist. , vol.22 , pp. 118-184
    • Stone, C.J.1
  • 36
    • 0347351336 scopus 로고    scopus 로고
    • On adaptive function estimation
    • Submitted to
    • Yang, Y. (1997). On adaptive function estimation. Submitted to Ann. Statist.
    • (1997) Ann. Statist.
    • Yang, Y.1
  • 37
    • 0346090207 scopus 로고    scopus 로고
    • Information-theoretic determination of minimax rates of convergence
    • Submitted to
    • Yang, Y. and Barron, A. R. (1997). Information-theoretic determination of minimax rates of convergence. Submitted to Ann. Statist.
    • (1997) Ann. Statist.
    • Yang, Y.1    Barron, A.R.2
  • 38
    • 0031672252 scopus 로고    scopus 로고
    • An asymptotic property of model selection criteria
    • Yang, Y. and Barron, A. R. (1998). An asymptotic property of model selection criteria. IEEE Trans. Inform. Theory 44, 95-116.
    • (1998) IEEE Trans. Inform. Theory , vol.44 , pp. 95-116
    • Yang, Y.1    Barron, A.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.