IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v65y2003i4p411-417.html
   My bibliography  Save this article

Total error in a plug-in estimator of level sets

Author

Listed:
  • Baíllo, Amparo

Abstract

Given a density f, the minimum volume set of probability [alpha] can be estimated by the corresponding minimum volume set of a kernel estimator. We obtain convergence rates for this set estimator with respect to a measure-based distance.

Suggested Citation

  • Baíllo, Amparo, 2003. "Total error in a plug-in estimator of level sets," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 411-417, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:411-417
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00294-3
    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. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    2. Einmahl, J. H.J. & Mason, D.M., 1992. "Generalized quantile processes," Other publications TiSEM b2a76bac-045d-457f-869f-d, Tilburg University, School of Economics and Management.
    3. Ilya S. Molchanov, 1998. "A Limit Theorem for Solutions of Inequalities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 235-242, March.
    4. Polonik, Wolfgang, 1997. "Minimum volume sets and generalized quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 1-24, July.
    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. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.
    2. Mammen, Enno & Polonik, Wolfgang, 2013. "Confidence regions for level sets," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 202-214.
    3. Chiwoo Park & Jianhua Z. Huang & Yu Ding, 2010. "A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection," Operations Research, INFORMS, vol. 58(5), pages 1469-1480, October.
    4. Baíllo, Amparo & Cuevas, Antonio, 2003. "Parametric versus nonparametric tolerance regions indetection problems," DES - Working Papers. Statistics and Econometrics. WS ws037017, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Cholaquidis, Alejandro & Fraiman, Ricardo & Moreno, Leonardo, 2022. "Level set and density estimation on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

    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. Baíllo, Amparo, 2003. "Total error in a plug-in estimator of level sets," DES - Working Papers. Statistics and Econometrics. WS ws032806, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    3. Cadre, BenoI^t, 2006. "Kernel estimation of density level sets," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 999-1023, April.
    4. Polonik, Wolfgang & Yao, Qiwei, 2002. "Set-Indexed Conditional Empirical and Quantile Processes Based on Dependent Data," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 234-255, February.
    5. Ren, Qunshu & Mojirsheibani, Majid, 2008. "Nonparametric estimation of level sets under minimal assumptions," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3029-3033, December.
    6. Mammen, Enno & Polonik, Wolfgang, 2013. "Confidence regions for level sets," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 202-214.
    7. Di Bucchianico, A. & Einmahl, J.H.J. & Mushkudiani, N.A., 2001. "Smallest nonparametric tolerance regions," Other publications TiSEM 436f9be2-d0ad-49af-b6df-9, Tilburg University, School of Economics and Management.
    8. Cholaquidis, Alejandro & Fraiman, Ricardo & Moreno, Leonardo, 2022. "Level set and density estimation on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    9. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.
    10. Elena Di Bernardino & Thomas Laloë & Véronique Maume-Deschamps & Clémentine Prieur, 2013. "Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory," Post-Print hal-00580624, HAL.
    11. Gu, Jiaying & Russell, Thomas M., 2023. "Partial identification in nonseparable binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 528-562.
    12. Pavlides, Marios G. & Wellner, Jon A., 2012. "Nonparametric estimation of multivariate scale mixtures of uniform densities," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 71-89.
    13. Di, J. & Kolaczyk, E., 2010. "Complexity-penalized estimation of minimum volume sets for dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1910-1926, October.
    14. Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2015. "Inference on sets in finance," Quantitative Economics, Econometric Society, vol. 6(2), pages 309-358, July.
    15. Baíllo, Amparo & Cuesta-Albertos, Juan A. & Cuevas, Antonio, 2001. "Convergence rates in nonparametric estimation of level sets," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 27-35, May.
    16. Giovanni Paolo Crespi & Elisa Mastrogiacomo, 2020. "Qualitative robustness of set-valued value-at-risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 25-54, February.
    17. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    18. Kaido, Hiroaki & Molinari, Francesca & Stoye, Jörg, 2022. "Constraint Qualifications In Partial Identification," Econometric Theory, Cambridge University Press, vol. 38(3), pages 596-619, June.
    19. Vladimir I. Koltchinskii, 1998. "Differentiability of Inverse Operators and Limit Theorems for Inverse Functions," Journal of Theoretical Probability, Springer, vol. 11(3), pages 645-699, July.
    20. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    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:65:y:2003:i:4:p:411-417. 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.