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Sharp oracle bounds for monotone and convex regression through aggregation

Author

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Yuling Yan & Weijie J. Su & Jianqing Fan, 2023. "The Isotonic Mechanism for Exponential Family Estimation," Papers 2304.11160, arXiv.org, revised Oct 2023.

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