Using Prior Information about Population Quantiles in Nite Population Sampling Using Prior Information about Population Quantiles in Nite Population Sampling

SUMMARY Consider the problem of estimating the population mean when it is known a priori that the population median belongs to some interval. More generally consider the problem of estimating the population mean when it is known a priori that the median of some auxiliary variable belongs to some interval. In this note we show how the Polya posterior, which is useful in problems where little prior information is available, can be adapted to these new situations. The resulting point and interval estimators are shown to have good frequentist properties.