IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v83y2013i12p2711-2720.html
   My bibliography  Save this article

Pointwise and uniform convergence of kernel density estimators using random bandwidths

Author

Listed:
  • Dutta, Santanu
  • Goswami, Alok

Abstract

We obtain the rates of pointwise and uniform convergence of kernel density estimators using random bandwidths under i.i.d. as well as strongly mixing dependence assumptions. Pointwise rates are faster and not affected by the tail of the density.

Suggested Citation

  • Dutta, Santanu & Goswami, Alok, 2013. "Pointwise and uniform convergence of kernel density estimators using random bandwidths," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2711-2720.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2711-2720
    DOI: 10.1016/j.spl.2013.09.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213003088
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.09.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Wied, Dominik & Weißbach, Rafael, 2010. "Consistency of the kernel density estimator - a survey," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 53(1), pages 1-21.
    2. Mielniczuk, Jan, 1990. "Remark concerning data-dependent bandwidth choice in density estimation," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 27-33, January.
    3. Dominik Wied & Rafael Weißbach, 2012. "Consistency of the kernel density estimator: a survey," Statistical Papers, Springer, vol. 53(1), pages 1-21, February.
    4. Bose, Arup & Dutta, Santanu, 2013. "Density estimation using bootstrap bandwidth selector," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 245-256.
    5. Salim Lardjane, 2007. "Nonparametric density estimation for nonmixing approximable Stochastic Processes," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 209-221, October.
    6. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
    Full references (including those not matched with items on IDEAS)

    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. R. Zamini & V. Fakoor & M. Sarmad, 2015. "On estimation of a density function in multiplicative censoring," Statistical Papers, Springer, vol. 56(3), pages 661-676, August.
    2. Romain Azaïs & Alexandre Genadot, 2015. "Semi-parametric inference for the absorption features of a growth-fragmentation model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 341-360, June.
    3. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    4. Matthew A. Masten & Alexandre Poirier, 2020. "Inference on breakdown frontiers," Quantitative Economics, Econometric Society, vol. 11(1), pages 41-111, January.
    5. del Rio, Alejandro Quintela, 1996. "Comparison of bandwidth selectors in nonparametric regression under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 563-580, May.
    6. Eibelshäuser, Steffen & Wilhelm, Sascha, 2017. "Markets Take Breaks: Dynamic Price Competition with Opening Hours," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168247, Verein für Socialpolitik / German Economic Association.
    7. David Atienza & Pedro Larrañaga & Concha Bielza, 2022. "Rejoinder on: Hybrid semiparametric Bayesian networks," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 344-347, June.
    8. T. Sclocco & M. Marzio, 2001. "A note on kernel density estimation for non-negative random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 67-79, January.
    9. Miśkiewicz, Janusz, 2016. "Improving quality of sample entropy estimation for continuous distribution probability functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 473-485.
    10. Jos'e E. Figueroa-L'opez & Cheng Li, 2016. "Optimal Kernel Estimation of Spot Volatility of Stochastic Differential Equations," Papers 1612.04507, arXiv.org.
    11. Wen-Ching Wang, 2018. "Setting up evaluate indicators for slope control engineering based on spatial clustering analysis," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 93(2), pages 921-939, September.
    12. Nassira Menni & Abdelkader Tatachak, 2018. "A note on estimating the conditional expectation under censoring and association: strong uniform consistency," Statistical Papers, Springer, vol. 59(3), pages 1009-1030, September.
    13. Emili Tortosa-Ausina, 2000. "Inefficient banks or inefficient assets," Working Papers 0005, Departament Empresa, Universitat Autònoma de Barcelona, revised Dec 2000.
    14. Geng, Pei, 2022. "Estimation of functional-coefficient autoregressive models with measurement error," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    15. J. S. Marron & S. S. Chung, 2001. "Presentation of smoothers: the family approach," Computational Statistics, Springer, vol. 16(1), pages 195-207, March.
    16. Filippone, Maurizio & Sanguinetti, Guido, 2011. "Approximate inference of the bandwidth in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3104-3122, December.
    17. Farmen, Mark & Marron, J. S., 1999. "An assessment of finite sample performance of adaptive methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 143-168, April.
    18. Tepegjozova Marija & Zhou Jing & Claeskens Gerda & Czado Claudia, 2022. "Nonparametric C- and D-vine-based quantile regression," Dependence Modeling, De Gruyter, vol. 10(1), pages 1-21, January.
    19. Wang, Fahui & Antipova, Anzhelika & Porta, Sergio, 2011. "Street centrality and land use intensity in Baton Rouge, Louisiana," Journal of Transport Geography, Elsevier, vol. 19(2), pages 285-293.
    20. C. Sánchez-Sellero & W. González-Manteiga & R. Cao, 1999. "Bandwidth Selection in Density Estimation with Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 51-70, March.

    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:stapro:v:83:y:2013:i:12:p:2711-2720. 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/622892/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.