IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v71y2013i1p39-62.html
   My bibliography  Save this article

Optimal unbiased estimation of some population central moments

Author

Listed:
  • Mariano Ruiz Espejo
  • Miguel Delgado Pineda
  • Saralees Nadarajah

    ()

Abstract

In this paper, we have treated the problem of estimating some population central moments under distribution-free setting. Uniformly minimum variance unbiased estimators for some population central moments have been derived. Some examples of unbiased estimators of central moments have been given under various sampling designs such as simple random sampling with replacement (srsr) or without replacement (srs), probability proportional to size with replacement (ppsr) and probability graduated variable proportional to size without replacement (pgvps). An optimal unbiased estimator of the third population central moment is proposed and extended to some real situations. Some optimal unbiased estimators of the fourth population central moment are given. Several optimal unbiased estimators of the variance of the “sample quasivariance estimator” are identified. Finally, computer programs in R implementing all of the estimators are given. Copyright Sapienza Università di Roma 2013

Suggested Citation

  • Mariano Ruiz Espejo & Miguel Delgado Pineda & Saralees Nadarajah, 2013. "Optimal unbiased estimation of some population central moments," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 39-62, June.
  • Handle: RePEc:spr:metron:v:71:y:2013:i:1:p:39-62
    DOI: 10.1007/s40300-013-0006-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40300-013-0006-z
    Download Restriction: Access to full text is restricted to subscribers.

    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. Sarjinder Singh, 2001. "Generalized Calibration Approach for Estimating Variance in Survey Sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 404-417, June.
    2. Cem Kadilar & Yesim Unyazici & Hulya Cingi, 2009. "Ratio estimator for the population mean using ranked set sampling," Statistical Papers, Springer, vol. 50(2), pages 301-309, March.
    3. Annaliisa Kankainen & Sara Taskinen & Hannu Oja, 2007. "Tests of multinormality based on location vectors and scatter matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 357-379, November.
    4. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality-Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263.
    5. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    6. Guiso, Luigi & Jappelli, Tullio & Pistaferri, Luigi, 2002. "An Empirical Analysis of Earnings and Employment Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 241-253, April.
    7. Campbell Harvey & John Liechty & Merrill Liechty & Peter Muller, 2010. "Portfolio selection with higher moments," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 469-485.
    Full references (including those not matched with items on IDEAS)

    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:spr:metron:v:71:y:2013:i:1:p:39-62. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.