Coordination of Conditional Poisson Samples

Abstract

Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP) sampling is a modification of the classical Poisson sampling that produces a fixed-size pps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

A sample coordination method to monitor totals of environmental variables

“…The general framework of sample coordination was summarized by Grafström and Matei (2015). Here, we only consider the situation where we select samples from the same population U at different time occasions.…”

“…Coordination of well spread samples using the SCPS was introduced for finite populations by Grafström and Matei (2018b). A coordination method based on PRN is used in the algorithm, where the random number associated with each unit in the algorithm of SCPS remains over time, that is, r i (1) = r i (2) = r i for two time occasions.…”