IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i2p275-298.html
   My bibliography  Save this article

Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes

Author

Listed:
  • Lei, Liangzhen
  • Wu, Liming

Abstract

In this paper, we consider a uniformly ergodic Markov process (Xn)n[greater-or-equal, slanted]0 valued in a measurable subset E of Rd with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in L1(Rd,dx) and for , and the asymptotic optimality in the Bahadur sense. These generalize the known results in the i.i.d. case.

Suggested Citation

  • Lei, Liangzhen & Wu, Liming, 2005. "Large deviations of kernel density estimator in L1(Rd) for uniformly ergodic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 275-298, February.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:2:p:275-298
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00139-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bosq, Denis & Merlevède, Florence & Peligrad, Magda, 1999. "Asymptotic Normality for Density Kernel Estimators in Discrete and Continuous Time," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 78-95, January.
    2. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    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. Gao, Fuqing, 2008. "Moderate deviations and law of the iterated logarithm in for kernel density estimators," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 452-473, March.

    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. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR‐GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    2. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    3. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    4. Conrad, Christian & Mammen, Enno, 2016. "Asymptotics for parametric GARCH-in-Mean models," Journal of Econometrics, Elsevier, vol. 194(2), pages 319-329.
    5. Taisuke Otsu & Myung Hwan Seo, 2014. "Asymptotics for maximum score method under general conditions," STICERD - Econometrics Paper Series 571, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    7. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
    8. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    9. Piotr Kokoszka & Michael Wolf, 2002. "Subsampling the mean of heavy-tailed dependent observations," Economics Working Papers 600, Department of Economics and Business, Universitat Pompeu Fabra.
    10. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    11. Fernandes, Marcelo, 2004. "Bounds for the probability distribution function of the linear ACD process," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 169-176, June.
    12. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2020. "On an integer-valued stochastic intensity model for time series of counts," MPRA Paper 105406, University Library of Munich, Germany.
    13. Storti, G., 2006. "Minimum distance estimation of GARCH(1,1) models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1803-1821, December.
    14. Marcelo Cunha Medeiros & Alvaro Veiga, 2004. "Modelling multiple regimes in financial volatility with a flexible coefficient GARCH model," Textos para discussão 486, Department of Economics PUC-Rio (Brazil).
    15. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    16. Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
    17. repec:kan:wpaper:202105 is not listed on IDEAS
    18. repec:bla:jecsur:v:22:y:2008:i:4:p:711-751 is not listed on IDEAS
    19. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    20. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    21. M. Sköld, 2001. "The Asymptotic Variance of the Continuous-Time Kernel Estimator with Applications to Bandwidth Selection," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 99-117, January.
    22. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.

    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:eee:spapps:v:115:y:2005:i:2:p:275-298. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.