Large-Sample Posterior Distributions for Finite Populations

Abstract

One of the strongest features of conventional sample survey theory is that very little needs to be assumed about the form of the population distribution. Hartley and Rao (1968) and Ericson (1969) have recently developed a Bayesian approach to sampling from finite populations that shares this feature. In this note, the resulting posterior distribution of the population elements is shown to approach normality for a broad class of prior distributions when the population size $N$ and sample size $n$ increase so that $n \rightarrow \infty$ and $N - n \rightarrow \infty$. In most cases this leads to the same large-sample interval estimates for population moments as the usual approach invoking the Central Limit Theorem for random sampling from a finite population (Madow (1948), Erdos and Renyi (1958), Hajek (1960)).