IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v13y1982i1p11-25.html
   My bibliography  Save this article

Limit theorems for stochastic measures of the accuracy of density estimators

Author

Listed:
  • Hall, Peter

Abstract

Stochastic measures of the distance between a density f and its estimate fn have been used to compare the accuracy of density estimators in Monte Carlo trials. The practice in the past has been to select a measure largely on the basis of its ease of computation, using only heuristic arguments to explain the large sample behaviour of the measure. Steele [11] has shown that these arguments can lead to incorrect conclusions. In the present paper we obtain limit theorems for the stochastic processes derived from stochastic measures, thereby explaining the large sample behaviour of the measures.

Suggested Citation

  • Hall, Peter, 1982. "Limit theorems for stochastic measures of the accuracy of density estimators," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 11-25, July.
    • Handle: RePEc:eee:spapps:v:13:y:1982:i:1:p:11-25
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(82)90003-5
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Biao, 1998. "A note on the integrated square errors of kernel density estimators under random censorship," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 225-234, July.
    2. Bruce Bloxom, 1985. "A constrained spline estimator of a hazard function," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 301-321, September.
    3. Małgorzata Łazȩcka & Jan Mielniczuk, 2023. "Squared error-based shrinkage estimators of discrete probabilities and their application to variable selection," Statistical Papers, Springer, vol. 64(1), pages 41-72, February.
    4. Fakoor, Vahid & Jomhoori, Sarah & Azarnoosh, Hasanali, 2009. "Asymptotic expansion for ISE of kernel density estimators under censored dependent model," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1809-1817, September.
    5. Chernova, O. & Lavancier, F. & Rochet, P., 2020. "Averaging of density kernel estimators," Statistics & Probability Letters, Elsevier, vol. 158(C).
    6. Majid Mojirsheibani & William Pouliot, 2017. "Weighted bootstrapped kernel density estimators in two-sample problems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 61-84, January.

    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:13:y:1982:i:1:p:11-25. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.