| dc.description.abstract | Abstract:
This paper considers the problem of estimating the population total in two-stage cluster sampling
when cluster sizes are unknown, making use of a population model arising basically from a variance
component model. The problem can be considered as one of predicting the unobserved part Z of the
total, and the concept of predictive likelihood is studied. Prediction intervals and a predictor for the
population total are derived for the normal case, based on predictive likelihood. The predictor
obtained from the predictive likelihood is shown to be approximately uniformly optimal for large
sample size and large number of clusters, in the sense of uniformly minimizing the mean square
error in a partially linear class of model-unbiased predictors. Three prediction intervals for Z based on
three similar predictive likelihoods are studied. For a small number n0 of sampled clusters they differ
significantly, however, for large n0 the three intervals are practically identical. Model-based and
design-based coverage properties of the prediction intervals are studied based on a comprehensive
simulation study. Roughly, the simulation study indicates that for large sample sizes the coverage
measures achieve approximately the nominal level 1 - á and are slightly less than 1 - á for
moderately large sample sizes. For small sample sizes the coverage measures are about 95% of the
nominal level.
Keywords: Survey sampling, population model, predictive likelihood, optimal predictor, prediction
intervals, simulation | no_NO |
