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Asymptotically efficient estimates for nonparametric regression models

Author

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  • Galtchouk, L.
  • Pergamenshchikov, S.

Abstract

The paper deals with estimating problem of regression function at a given state point in nonparametric regression models with Gaussian noises and with non-Gaussian noises having unknown distribution. An asymptotically efficient kernel estimator is constructed for a minimax risk.

Suggested Citation

  • Galtchouk, L. & Pergamenshchikov, S., 2006. "Asymptotically efficient estimates for nonparametric regression models," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 852-860, April.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:8:p:852-860
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    References listed on IDEAS

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    1. 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.
    2. E. Belitser, 2000. "Local minimax pointwise estimation of a multivariate density," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 351-365, November.
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    Citations

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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. Peng, Jingfu, 2023. "Adaptive and efficient estimation in the Gaussian sequence model," Statistics & Probability Letters, Elsevier, vol. 195(C).
    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, 2010. "General model selection estimation of a periodic regression with a Gaussian noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 1083-1111, December.
    5. 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.
    6. J.-Y. Brua, 2009. "Adaptive estimators for nonparametric heteroscedastic regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 991-1002.

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