Prediction with measurement errors in finite populations |
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Authors: | Singer Julio M Stanek Edward J Lencina Viviana B González Luz Mery Li Wenjun Martino Silvina San |
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Affiliation: | a Departamento de Estatística, Universidade de São Paulo, Brazilb Department of Public Health, University of Massachusetts at Amherst, USAc Facultad de Ciencias Economicas, Universidad Nacional de Tucumán, CONICET, Argentinad Departamento de Estadística, Universidad Nacional de Colombia, Bogotá, Colombiae Division of Preventive and Behavioral Medicine, University of Massachusetts, Worcester, USAf Facultad de Ciencias Agrarias, Universidad Nacional de Mar del Plata, Argentina |
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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. |
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Keywords: | Finite population Heteroskedasticity Superpopulation Unbiasedness |
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