Prediction with measurement errors in finite populations

UMMS Affiliation

Department of Medicine, Division of Preventive and Behavioral Medicine

Publication Date


Document Type



Statistics and Probability


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 point to some difficulties in the interpretation of such predictors.

DOI of Published Version



Singer JM, Stanek EJ 3rd, Lencina VB, González LM, Li W, Martino SS. Prediction with measurement errors in finite populations. Stat Probab Lett. 2012 Feb 1;82(2):332-339. Link to article on publisher's site

Journal/Book/Conference Title

Statistics and probability letters

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Link to Article in PubMed

PubMed ID