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Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models

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  • L. Galtchouk
  • S. Pergamenshchikov

Abstract

An adaptive non-parametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (oracle inequality) is obtained.

Suggested Citation

  • L. Galtchouk & S. Pergamenshchikov, 2009. "Sharp non-asymptotic oracle inequalities for non-parametric heteroscedastic regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 1-18.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:1:p:1-18
    DOI: 10.1080/10485250802504096
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    References listed on IDEAS

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    1. Akritas M. G & Van Keilegom I., 2001. "ANCOVA Methods for Heteroscedastic Nonparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 220-232, March.
    2. L. Galtchouk & S. Pergamenshchikov, 2006. "Asymptotically Efficient Sequential Kernel Estimates of the Drift Coefficient in Ergodic Diffusion Processes," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 1-16, May.
    3. Rohde Angelika, 2004. "On the asymptotic equivalence and rate of convergence of nonparametric regression and Gaussian white noise," Statistics & Risk Modeling, De Gruyter, vol. 22(3), pages 235-243, March.
    4. D. Fourdrinier & S. Pergamenshchikov, 2007. "Improved Model Selection Method for a Regression Function with Dependent Noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 435-464, September.
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    Cited by:

    1. E. A. Pchelintsev & S. M. Pergamenshchikov, 2018. "Oracle inequalities for the stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 469-483, July.
    2. Evgeny Pchelintsev & Serguei Pergamenshchikov & Maria Leshchinskaya, 2022. "Improved estimation method for high dimension semimartingale regression models based on discrete data," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 537-576, October.
    3. Slim Beltaief & Oleg Chernoyarov & Serguei Pergamenchtchikov, 2020. "Model selection for the robust efficient signal processing observed with small Lévy noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1205-1235, October.
    4. Victor, Konev & Serguei, Pergamenchtchikov, 2015. "Robust model selection for a semimartingale continuous time regression from discrete data," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 294-326.
    5. Liyun Su & Yanyong Zhao & Tianshun Yan & Fenglan Li, 2012. "Local Polynomial Estimation of Heteroscedasticity in a Multivariate Linear Regression Model and Its Applications in Economics," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.

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