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Abstract:
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We present a parametric approach for the estimation of enumerative finite population characteristics such as totals and means for complex survey samples in the presence of full response. We go beyond the model-assisted design approach by estimating the parameters of the distribution of the working model that generates the finite population while taking into account the sample design. Through statistical tests of parameters and model goodness of fit, we are able to determine the functional form of the estimator and the relevant set of auxiliary variables. Since this approach makes use of an explicit model for the finite population generating process, it can incorporate most recent developments in modeling from classical statistics. This approach is only based on the observed sample and does not rely on simulation studies for comparing models and evaluating estimators. We describe the foundations of the parametric estimation for finite populations based on sample-based maximum likelihood, present examples for finding efficient estimators and selecting auxiliary variables, and describe the effect on model misspecification on the statistical properties of estimates.
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