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Successive sampling discovery problems arise in finite population sampling subject to 'size-biased' selection mechanisms.
The asymptotic properties of the estimators are studied using martingales, modern empirical process theory, and results for finite population sampling.
A useful concept in finite population sampling is stratification.
The most important quantity of interest in finite population sampling is usually the population total or the population mean.
We provide some optimality results and show that, in the context of finite population sampling, maxima nomination sampling is not generally the optimum design to follow.
Bayesian inference in finite population sampling is independent of the choice of the sampling design, because the posterior distribution remains invariant with respect to the choice of the sampling design.
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Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119 130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models.
This chapter introduces terminologies and basic concepts of sampling from finite populations such as sampling design, inclusion probabilities, ordered and unordered samples, and sampling schemes.
When estimating model parameters from survey data, two sources of variability should normally be taken into account for inference purposes: the model that is assumed to have generated data of the finite population, and the sampling design.
The finite population correction and sampling weight were incorporated into the analysis.
Note that pseudo-coverage is equal to the true coverage for the finite population of 69 samples.
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