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Regularization in statistics

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Author Info

  • Peter Bickel

    ()

  • Bo Li
  • Alexandre Tsybakov
  • Sara Geer
  • Bin Yu
  • Teófilo Valdés
  • Carlos Rivero
  • Jianqing Fan
  • Aad Vaart

Abstract

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File URL: http://hdl.handle.net/10.1007/BF02607055
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Bibliographic Info

Article provided by Springer in its journal Test.

Volume (Year): 15 (2006)
Issue (Month): 2 (September)
Pages: 271-344

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Handle: RePEc:spr:testjl:v:15:y:2006:i:2:p:271-344

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Related research

Keywords: Regularization; linear regression; nonparametric regression; boosting; covariance matrix; principal component; bootstrap; subsampling; model selection; Primary 62G08; 62H12; Secondary 62F12; 62G20; 62H25;

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References

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  1. Michael J. Daniels, 2002. "Bayesian analysis of covariance matrices and dynamic models for longitudinal data," Biometrika, Biometrika Trust, vol. 89(3), pages 553-566, August.
  2. Hao Helen Zhang & Grace Wahba & Yi Lin & Meta Voelker & Michael Ferris & Ronald Klein & Barbara Klein, 2004. "Variable Selection and Model Building via Likelihood Basis Pursuit," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 659-672, January.
  3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
  4. Gábor Lugosi & Andrew B. Nobel, 1998. "Adaptive model selection using empirical complexities," Economics Working Papers 323, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
  6. Carlos Rivero & Teófilo Valdés, 2004. "Mean-Based Iterative Procedures in Linear Models with General Errors and Grouped Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 469-486.
  7. Bair, Eric & Hastie, Trevor & Paul, Debashis & Tibshirani, Robert, 2006. "Prediction by Supervised Principal Components," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 119-137, March.
  8. Fan, Jianqing & Peng, Heng & Huang, Tao, 2005. "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 781-796, September.
  9. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
  10. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
  11. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
  12. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, vol. 90(4), pages 831-844, December.
  13. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  14. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  15. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
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Citations

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Cited by:
  1. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(2), pages 183-221, June.
  2. Politis, Dimitris N, 2010. "Model-free Model-fitting and Predictive Distributions," University of California at San Diego, Economics Working Paper Series qt67j6s174, Department of Economics, UC San Diego.
  3. Ignacio González & Sébastien Déjean & Pascal G. P. Martin & Alain Baccini, . "CCA: An R Package to Extend Canonical Correlation Analysis," Journal of Statistical Software, American Statistical Association, vol. 23(i12).

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