IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2015-04.html

Sharp oracle bounds for monotone and convex regression through aggregation

Author

Listed:
  • Pierre Bellec

    (CREST, ENSAE, UMR CNRS 9194)

  • Alexandre Tsybakov

    (CREST, ENSAE, UMR CNRS 9194)

Abstract

We derive oracle inequalities for the problems of isotonic and convex regression using the combination of Q-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities for the constrained least squares estimator. One of the improvements is that our oracle inequalities are sharp, i.e., with leading constant 1. It allows us to obtain bounds for the minimax regret thus accounting for model misspecification, which was not possible based on the previous results. Another improvement is that we obtain oracle inequalities both with high probability and in expectation.

Suggested Citation

  • Pierre Bellec & Alexandre Tsybakov, 2015. "Sharp oracle bounds for monotone and convex regression through aggregation," Working Papers 2015-04, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2015-04
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2015-04.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Arnak S. Dalalyan & Mohamed Hebiri & Johannes Lederer, 2014. "On the Prediction Performance of the Lasso," Working Papers 2014-05, Center for Research in Economics and Statistics.
    2. Alexander Rakhlin & Karthik Sridharan & Alexandre Tsybakov, 2013. "Empirical Entropy, Minimax Regret and Minimax Risk," Working Papers 2013-38, Center for Research in Economics and Statistics.
    3. Tingni Sun & Cun-Hui Zhang, 2012. "Scaled sparse linear regression," Biometrika, Biometrika Trust, vol. 99(4), pages 879-898.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuling Yan & Weijie J. Su & Jianqing Fan, 2023. "Isotonic Mechanism for Exponential Family Estimation in Machine Learning Peer Review," Papers 2304.11160, arXiv.org, revised Feb 2025.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rahul Mazumder & Peter Radchenko & Antoine Dedieu, 2023. "Subset Selection with Shrinkage: Sparse Linear Modeling When the SNR Is Low," Operations Research, INFORMS, vol. 71(1), pages 129-147, January.
    2. Tung Duy Luu & Jalal Fadili & Christophe Chesneau, 2020. "Sharp oracle inequalities for low-complexity priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 353-397, April.
    3. Laura Freijeiro‐González & Manuel Febrero‐Bande & Wenceslao González‐Manteiga, 2022. "A Critical Review of LASSO and Its Derivatives for Variable Selection Under Dependence Among Covariates," International Statistical Review, International Statistical Institute, vol. 90(1), pages 118-145, April.
    4. Jacob Bien & Irina Gaynanova & Johannes Lederer & Christian L. Müller, 2019. "Prediction error bounds for linear regression with the TREX," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 451-474, June.
    5. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    6. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    7. Pierre Bellec, 2015. "Optimal bounds for aggregation of affine estimators," Working Papers 2015-06, Center for Research in Economics and Statistics.
    8. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    9. Xie, Jichun & Kang, Jian, 2017. "High-dimensional tests for functional networks of brain anatomic regions," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 70-88.
    10. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    11. Donnat, Claire & Klopp, Olga & Verzelen, Nicolas, 2026. "Denoising over networks with applications to partially observed epidemics," Computational Statistics & Data Analysis, Elsevier, vol. 215(C).
    12. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.
    13. Zehua Chen & Yiwei Jiang, 2020. "A two-stage sequential conditional selection approach to sparse high-dimensional multivariate regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 65-90, February.
    14. Wang, Yihe & Zhao, Sihai Dave, 2021. "A nonparametric empirical Bayes approach to large-scale multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    15. Victor Chernozhukov & Christian Hansen & Yuan Liao, 2015. "A lava attack on the recovery of sums of dense and sparse signals," CeMMAP working papers CWP56/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Gueuning, Thomas & Claeskens, Gerda, 2016. "Confidence intervals for high-dimensional partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 13-29.
    17. Zhou, Jia & Zheng, Zemin & Zhou, Huiting & Dong, Ruipeng, 2021. "Innovated scalable efficient inference for ultra-large graphical models," Statistics & Probability Letters, Elsevier, vol. 173(C).
    18. Lan, Wei & Zhong, Ping-Shou & Li, Runze & Wang, Hansheng & Tsai, Chih-Ling, 2016. "Testing a single regression coefficient in high dimensional linear models," Journal of Econometrics, Elsevier, vol. 195(1), pages 154-168.
    19. Zeyu Wu & Cheng Wang & Weidong Liu, 2023. "A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 619-648, August.
    20. Wanling Xie & Hu Yang, 2023. "Group sparse recovery via group square-root elastic net and the iterative multivariate thresholding-based algorithm," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 469-507, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2015-04. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.