Bootstrap Methods for Finite Populations

Abstract

Abstract We show that the familiar bootstrap plug-in rule of Efron has a natural analog in finite population settings. In our method a characteristic of the population is estimated by the average value of the characteristic over a class of empirical populations constructed from the sample. Our method extends that of Gross to situations in which the stratum sizes are not integer multiples of their respective sample sizes. Moreover, we show that our method can be used to generate second-order correct confidence intervals for smooth functions of population means, a property that has not been established for other resampling methods suggested in the literature. A second resampling method is proposed that also leads to second-order correct confidence intervals and is less computationally intensive than our bootstrap. But a simulation study reveals that the second method can be quite unstable in some situations, whereas our bootstrap performs very well.