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Uniform Rates for Kernel Estimators of Weakly Dependent Data

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  • Juan Carlos Escanciano

Abstract

This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are useful for establishing asymptotic theory for two-step semiparametric estimators in time series models. We apply our results to obtain nonparametric estimates and their rates for Expected Shortfall processes.

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  • Juan Carlos Escanciano, 2020. "Uniform Rates for Kernel Estimators of Weakly Dependent Data," Papers 2005.09951, arXiv.org.
    • Handle: RePEc:arx:papers:2005.09951
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    References listed on IDEAS

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    1. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    2. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129, January.
    3. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    4. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    5. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1433-1445, October.
    6. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    7. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    8. Juan Carlos Escanciano & Lin Zhu, 2015. "A Simple Data-Driven Estimator for the Semiparametric Sample Selection Model," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 734-762, December.
    9. Juan Carlos Escanciano & Silvia Mayoral, 2008. "Semiparametric estimation of dynamic conditional expected shortfall models," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 1(2), pages 106-120.
    10. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(3), pages 560-586, June.
    11. Nze, Patrick Ango & Doukhan, Paul, 2004. "Weak Dependence: Models And Applications To Econometrics," Econometric Theory, Cambridge University Press, vol. 20(6), pages 995-1045, December.
    12. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    13. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1529-1564, October.
    14. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    15. Linton, Oliver & Xiao, Zhijie, 2013. "Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 29(4), pages 771-807, August.
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    Cited by:

    1. Luis Alvarez & Cristine Pinto, 2023. "A maximal inequality for local empirical processes under weak dependence," Papers 2307.01328, arXiv.org.

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