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Regularization in statistics

Author

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

Abstract

No abstract is available for this item.

Suggested Citation

  • Peter Bickel & Bo Li & Alexandre Tsybakov & Sara Geer & Bin Yu & Teófilo Valdés & Carlos Rivero & Jianqing Fan & Aad Vaart, 2006. "Regularization in statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(2), pages 271-344, September.
    • Handle: RePEc:spr:testjl:v:15:y:2006:i:2:p:271-344
    DOI: 10.1007/BF02607055
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    References listed on IDEAS

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    1. 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.
    2. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    3. Gábor Lugosi & Andrew B. Nobel, 1998. "Adaptive model selection using empirical complexities," Economics Working Papers 323, Department of Economics and Business, Universitat Pompeu Fabra.
    4. 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, September.
    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. 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.
    7. 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.
    8. 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.
    9. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Wei Biao Wu, 2003. "Nonparametric estimation of large covariance matrices of longitudinal data," Biometrika, Biometrika Trust, vol. 90(4), pages 831-844, December.
    15. 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.
    16. 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, April.
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    Citations

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    Cited by:

    1. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    2. Dimitri Yatsenko & Krešimir Josić & Alexander S Ecker & Emmanouil Froudarakis & R James Cotton & Andreas S Tolias, 2015. "Improved Estimation and Interpretation of Correlations in Neural Circuits," PLOS Computational Biology, Public Library of Science, vol. 11(3), pages 1-28, March.
    3. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    4. Demian Pouzo, 2015. "On the Non-Asymptotic Properties of Regularized M-estimators," Papers 1512.06290, arXiv.org, revised Oct 2016.
    5. Gao, Wenwu & Wang, Jiecheng & Zhang, Ran, 2023. "Quasi-interpolation for multivariate density estimation on bounded domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 592-608.
    6. S. Barahona & P. Centella & X. Gual-Arnau & M. V. Ibáñez & A. Simó, 2020. "Supervised classification of geometrical objects by integrating currents and functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 637-660, September.
    7. Dimitris Politis, 2013. "Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 183-221, June.
    8. Hiroyuki Kawakatsu, 2022. "Modeling Realized Variance with Realized Quarticity," Stats, MDPI, vol. 5(3), pages 1-25, September.
    9. González, Ignacio & Déjean, Sébastien & Martin, Pascal G. P. & Baccini, Alain, 2008. "CCA: An R Package to Extend Canonical Correlation Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i12).
    10. van Wieringen, Wessel N. & Peeters, Carel F.W., 2016. "Ridge estimation of inverse covariance matrices from high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 284-303.
    11. Campbell R. Harvey & Yan Liu, 2016. "Rethinking Performance Evaluation," NBER Working Papers 22134, National Bureau of Economic Research, Inc.
    12. Nandana Sengupta & Fallaw Sowell, 2019. "The Ridge Path Estimator for Linear Instrumental Variables," Papers 1908.09237, arXiv.org.
    13. 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.
    14. Nandana Sengupta & Fallaw Sowell, 2020. "On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples," Econometrics, MDPI, vol. 8(4), pages 1-25, October.

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