Theory and Practice of Maximal Brewer Selection with Poisson PRN Sampling

摘要

K.R.W. Brewer suggests that when estimating the total of a single item for which there is control (auxiliary) data, one employ a ratio or regression estimator and draw the sample using probabilities proportional to the control values raised to a power between 1/2 and 1. Brewer's sample selection scheme can be expanded to multiple targets by drawing overlapping Poisson samples for a number of items simultaneously using permanent random numbers (PRN's). W e can call the result an example of 'Maximal Brewer Selection' (MBS). This paper develops the theory behind MBS and the calibration estimator rendering it practical. It goes on to describe how this estimation strategy is being used at the National Agricultural Statistics Service.