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Prediction with measurement errors in finite populations

Author

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

Abstract

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
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    References listed on IDEAS

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    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.
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    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.

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