IDEAS home Printed from
   My bibliography  Save this paper

On dispersion preserving estimation of the mean of a binary variable from small areas




Over-shrinkage is a common problem in small area (or domain) estimation. It happens when the estimated small-area parameters have less between-area variation than their true values. To deal with this problem, Louis (1984), Ghosh (1992) and Spjøtvoll and Thomsen (1987) have proposed various constrained empirical and hierarchical Bayes methods. In this paper we study two non-Bayesian methods based on, respectively, the synthetic estimator and a variance-component model. We show first that the synthetic estimator entails loss of dispersion in general, from which it follows that the coverage level of the confidence intervals could be far below the nominal level of confidence, when these are derived from the sampling error alone. A bivariate variance-component model at the area-level, as well as its simplification, can greatly improve the efficiency of the confidence intervals. However, super-population approaches as such are unable to capture the distribution of the true area-parameters. We develop a finite-population approach based on an empirical finite-population distribution function of the area-parameters, which provides the necessary adjustment. The various methods will be illustrated using the data of the Census 1990. Finally, we notice that several European countries will base the upcoming Census on their administrative register systems, instead of collecting the information in the field. Improved small area estimation methods may prove to be valuable for assessing the quality of such Register Counting.

Suggested Citation

  • Li-Chun Zhang, 2000. "On dispersion preserving estimation of the mean of a binary variable from small areas," Discussion Papers 285, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:285

    Download full text from publisher

    File URL:
    Download Restriction: no


    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:ssb:dispap:285. 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: (L Maasø) or (Rebekah McClure). General contact details of provider: .

    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 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.

    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.