Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 426-445

USING PRIOR INFORMATION ABOUT POPULATION QUANTILES IN FINITE POPULATION SAMPLING

By

DAVID NELSON, *Center for Chronic Disease Outcomes Research, Minneapolis*

and

GLEN MEEDEN, *University of Minnesota, Minneapolis*

*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.

*AMS (1991) subject classification. *Primary 62D05; secondary 62F15,
62C15.

*Key words and phrases. *Quantiles, stratification, Polya posterior, finite population sampling,
prior information and interval estimation.