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We develop best linear unbiased predictors (BLUP) of the latent values of labeled sample units selected from a finite population when there are two distinct sources of measurement error: endogenous, exogenous or both. Usual target parameters are the population mean, the latent values associated to a labeled unit or the latent value of the unit that will appear in a given position in the sample. We show how both types of measurement errors affect the within unit covariance matrices and indicate how the finite population BLUP may be obtained via standard software packages employed to fit mixed models in situations with either heteroskedastic or homoskedastic exogenous and endogenous measurement errors.
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