IDEAS home Printed from
   My bibliography  Save this article

Prediction with measurement errors in finite populations


  • Singer, Julio M.
  • Stanek, Edward J.
  • Lencina, Viviana B.
  • González, Luz Mery
  • Li, Wenjun
  • San Martino, Silvina


We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which points to some difficulties in the interpretation of such predictors.

Suggested Citation

  • Singer, Julio M. & Stanek, Edward J. & Lencina, Viviana B. & González, Luz Mery & Li, Wenjun & San Martino, Silvina, 2012. "Prediction with measurement errors in finite populations," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 332-339.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:2:p:332-339
    DOI: 10.1016/j.spl.2011.10.013

    Download full text from publisher

    File URL:
    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

    1. San Martino, Silvina & Singer, Julio M. & Stanek III, Edward J., 2008. "Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2199-2217, January.
    2. Edward J. Stanek & Julio M. Singer, 2004. "Predicting Random Effects From Finite Population Clustered Samples With Response Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1119-1130, December.
    Full references (including those not matched with items on IDEAS)


    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:82:y:2012:i:2:p:332-339. 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: (Dana Niculescu). 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.

    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.