Inference on Symmetric Functions of Exchangeable Populations
Roger A. Sugden · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1979
Summary A model is proposed for inference on symmetric functions of a finite population where the only prior information available is exchangeability of the unknown unit values. It is shown through sufficiency that the labels convey no information. When the sample size is fixed, the order statistic is complete as well as sufficient so that optimal estimators are symmetric. In particular, the sample mean is the minimum variance unbiased estimator of the population mean, averaging under the model being equivalent to averaging firstly over the sample design and then over all permutations of the units. A new subjective justification is therefore found for the use in practice of classical formulae based on simple random sampling, but now for any sample design.