메뉴 건너뛰기




Volumn 2, Issue 2, 2005, Pages 131-154

Asymptotics of cross-validated risk estimation in estimator selection and performance assessment

Author keywords

Asymptotic linearity; Asymptotic optimality; Classification; Confidence interval; Cross validation; Density estimation; Estimator selection; Generalization error; Indicator loss function; L2 loss function; Loss function; Model selection

Indexed keywords


EID: 26644446561     PISSN: 15723127     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.stamet.2005.02.003     Document Type: Article
Times cited : (147)

References (39)
  • 4
    • 0001587464 scopus 로고
    • The little bootstrap and other methods for dimensionality selection in regression: X-fixed prediction error
    • L. Breiman The little bootstrap and other methods for dimensionality selection in regression: x -fixed prediction error Journal of the American Statistical Association 87 419 1992 738 754
    • (1992) Journal of the American Statistical Association , vol.87 , Issue.419 , pp. 738-754
    • Breiman, L.1
  • 5
    • 0030344230 scopus 로고    scopus 로고
    • Heuristics of instability and stabilization in model selection
    • L. Breiman Heuristics of instability and stabilization in model selection Annals of Statistics 24 6 1996 2350 2383
    • (1996) Annals of Statistics , vol.24 , Issue.6 , pp. 2350-2383
    • Breiman, L.1
  • 6
    • 0004140497 scopus 로고    scopus 로고
    • Out-of-bag estimation
    • Department of Statistics, University of California, Berkeley
    • L. Breiman, Out-of-bag estimation, Technical Report, Department of Statistics, University of California, Berkeley, 1996
    • (1996) Technical Report
    • Breiman, L.1
  • 8
    • 0000343716 scopus 로고
    • Submodel selection and evaluation in regression: The x random case
    • L. Breiman, and P. Spector Submodel selection and evaluation in regression: the x random case International Statistical Review 60 1992 291 319
    • (1992) International Statistical Review , vol.60 , pp. 291-319
    • Breiman, L.1    Spector, P.2
  • 9
    • 0000354976 scopus 로고
    • A comparative study of ordinary cross-validation, v -fold cross-validation and the repeated learning-testing methods
    • P. Burman A comparative study of ordinary cross-validation, v -fold cross-validation and the repeated learning-testing methods Biometrika 76 1989 503 514
    • (1989) Biometrika , vol.76 , pp. 503-514
    • Burman, P.1
  • 12
    • 14644442781 scopus 로고    scopus 로고
    • Asymptotics of cross-validated risk estimation in model selection and performance assessment
    • Division of Biostatistics, University of California, Berkeley
    • S. Dudoit, M.J. van der Laan, Asymptotics of cross-validated risk estimation in model selection and performance assessment, Technical Report 126, Division of Biostatistics, University of California, Berkeley, 2003. URL: http://www.bepress.com/ucbbiostat/paper126
    • (2003) Technical Report , vol.126
    • Dudoit, S.1    Van Der Laan, M.J.2
  • 13
    • 33644749679 scopus 로고    scopus 로고
    • Loss-based estimation with cross-validation: Applications to microarray data analysis
    • G. Piatetsky-Shapiro P. Microarray Data Mining Tamayo
    • S. Dudoit, M.J. van der Laan, S. Keleş, A.M. Molinaro, S.E. Sinisi, and S.L. Teng Loss-based estimation with cross-validation: Applications to microarray data analysis G. Piatetsky-Shapiro P. Tamayo Microarray Data Mining SIGKDD Explorations 5 2 2003 56 68 ACM
    • (2003) SIGKDD Explorations , vol.5 , Issue.2 , pp. 56-68
    • Dudoit, S.1    Van Der Laan, M.J.2    Keleş, S.3    Molinaro, A.M.4    Sinisi, S.E.5    Teng, S.L.6
  • 14
    • 84950461478 scopus 로고
    • Estimating the error rate of a prediction rule: Improvement on cross-validation
    • B. Efron Estimating the error rate of a prediction rule: Improvement on cross-validation Journal of the American Statistical Association 78 1983 316 331
    • (1983) Journal of the American Statistical Association , vol.78 , pp. 316-331
    • Efron, B.1
  • 17
    • 0001552995 scopus 로고
    • Cross-validation, the jackknife, and the bootstrap: Excess error estimation in forward logistic regression
    • G. Gong Cross-validation, the jackknife, and the bootstrap: Excess error estimation in forward logistic regression Journal of the American Statistical Association 81 1986 108 113
    • (1986) Journal of the American Statistical Association , vol.81 , pp. 108-113
    • Gong, G.1
  • 18
    • 0005859021 scopus 로고    scopus 로고
    • On the asymptotic normality of a resubstitution error estimate
    • A. Rizzi M. Vichi H.H. Bock Springer
    • L. Györfi, and M. Horváth On the asymptotic normality of a resubstitution error estimate A. Rizzi M. Vichi H.H. Bock Advances in Data Science and Classification 1998 Springer 197 204
    • (1998) Advances in Data Science and Classification , pp. 197-204
    • Györfi, L.1    Horváth, M.2
  • 20
    • 0036670570 scopus 로고    scopus 로고
    • Relative stability of global errors of nonparametric function estimators
    • L. Györfi, D. Schäfer, and H. Walk Relative stability of global errors of nonparametric function estimators IEEE Transactions on Information Theory 48 8 2002 2230 2242
    • (2002) IEEE Transactions on Information Theory , vol.48 , Issue.8 , pp. 2230-2242
    • Györfi, L.1    Schäfer, D.2    Walk, H.3
  • 22
    • 23744446342 scopus 로고    scopus 로고
    • Asymptotically optimal model selection method with right censored outcomes
    • S. Keleş, M.J. van der Laan, and S. Dudoit Asymptotically optimal model selection method with right censored outcomes Bernoulli 10 6 2004 1011 1037
    • (2004) Bernoulli , vol.10 , Issue.6 , pp. 1011-1037
    • Keleş, S.1    Van Der Laan, M.J.2    Dudoit, S.3
  • 23
    • 0001462696 scopus 로고
    • l, cross-validation and generalized cross-validation: Discrete index set
    • K.-C. Li Asymptotic optimality for c p, c l, cross-validation and generalized cross-validation: Discrete index set Annals of Statistics 15 1987 958 975
    • (1987) Annals of Statistics , vol.15 , pp. 958-975
    • Li, K.-C.1
  • 24
    • 0043274627 scopus 로고
    • The use of balanced half-sample replication in cross-validation studies
    • P.J. McCarthy The use of balanced half-sample replication in cross-validation studies Journal of the American Statistical Association 71 1976 596 604
    • (1976) Journal of the American Statistical Association , vol.71 , pp. 596-604
    • McCarthy, P.J.1
  • 25
    • 23744457899 scopus 로고    scopus 로고
    • Tree-based multivariate regression and density estimation with right-censored data
    • S. Dudoit R.C. Gentleman M.J. van der Laan Multivariate Methods in Genomic Data Analysis
    • A.M. Molinaro, S. Dudoit, and M.J. van der Laan Tree-based multivariate regression and density estimation with right-censored data S. Dudoit R.C. Gentleman M.J. van der Laan Multivariate Methods in Genomic Data Analysis Journal of Multivariate Analysis 90 1 2004 154 177 Elsevier
    • (2004) Journal of Multivariate Analysis , vol.90 , Issue.1 , pp. 154-177
    • Molinaro, A.M.1    Dudoit, S.2    Van Der Laan, M.J.3
  • 26
    • 33644753223 scopus 로고    scopus 로고
    • Deletion/Substitution/Addition algorithm for partitioning the covariate space in prediction
    • Division of Biostatistics, University of California, Berkeley
    • A.M. Molinaro, M.J. van der Laan, Deletion/Substitution/Addition algorithm for partitioning the covariate space in prediction, Technical Report 162, Division of Biostatistics, University of California, Berkeley, 2004. URL: http://www.bepress.com/ucbbiostat/paper162
    • (2004) Technical Report , vol.162
    • Molinaro, A.M.1    Van Der Laan, M.J.2
  • 28
    • 0037031031 scopus 로고    scopus 로고
    • On the rate of convergence of error estimates for the partitioning classification rule
    • M. Pintér On the rate of convergence of error estimates for the partitioning classification rule Theoretical Computer Science 284 1 2002 181 196
    • (2002) Theoretical Computer Science , vol.284 , Issue.1 , pp. 181-196
    • Pintér, M.1
  • 31
    • 18544371304 scopus 로고    scopus 로고
    • Deletion/substitution/addition algorithm in learning with applications in genomics
    • S.E. Sinisi, and M.J. van der Laan Deletion/substitution/addition algorithm in learning with applications in genomics Statistical Applications in Genetics and Molecular Biology 3 1 2004 (Article 18). URL: http://www.bepress.com/sagmb/vol3/iss1/art18
    • (2004) Statistical Applications in Genetics and Molecular Biology , vol.3 , Issue.1
    • Sinisi, S.E.1    Van Der Laan, M.J.2
  • 32
    • 0000629975 scopus 로고
    • Cross-validatory choice and assessment of statistics predictions
    • M. Stone Cross-validatory choice and assessment of statistics predictions Journal of the Royal Statistical Society, Series B 36 2 1974 111 147
    • (1974) Journal of the Royal Statistical Society, Series B , vol.36 , Issue.2 , pp. 111-147
    • Stone, M.1
  • 33
    • 0017336301 scopus 로고
    • Asymptotics for and against cross-validation
    • M. Stone Asymptotics for and against cross-validation Biometrika 64 1 1977 29 35
    • (1977) Biometrika , vol.64 , Issue.1 , pp. 29-35
    • Stone, M.1
  • 34
    • 14644419415 scopus 로고    scopus 로고
    • Unified cross-validation methodology for selection among estimators and a general cross-validated adaptive ε-net estimator: Finite sample oracle inequalities and examples
    • Division of Biostatistics, University of California, Berkeley
    • M.J. van der Laan, S. Dudoit, Unified cross-validation methodology for selection among estimators and a general cross-validated adaptive ε -net estimator: Finite sample oracle inequalities and examples, Technical Report 130, Division of Biostatistics, University of California, Berkeley, 2003. URL: http://www.bepress.com/ucbbiostat/paper130
    • (2003) Technical Report , vol.130
    • Van Der Laan, M.J.1    Dudoit, S.2
  • 36
    • 14644397062 scopus 로고    scopus 로고
    • The cross-validated adaptive ε-net estimator
    • Division of Biostatistics, University of California, Berkeley
    • M.J. van der Laan, S Dudoit, A.W. van de Vaart, The cross-validated adaptive ε -net estimator, Technical Report 142, Division of Biostatistics, University of California, Berkeley, 2004. URL: http://www.bepress.com/ucbbiostat/paper142
    • (2004) Technical Report , vol.142
    • Van Der Laan, M.J.1    Dudoit, S.2    Van De Vaart, A.W.3
  • 39
    • 21144472438 scopus 로고
    • Model selection via multifold cross-validation
    • P. Zhang Model selection via multifold cross-validation Annals of Statistics 21 1993 299 313
    • (1993) Annals of Statistics , vol.21 , pp. 299-313
    • Zhang, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.