Poisson Mixture Sampling Combined with Order Sampling
Hannu Kröger, Carl-Erik Särndal, and Ismo Teikari
The term Poisson Mixture (PoMix) sampling refers to a family of sampling designs based on the Permanent Random Number (PRN) technique and useful for sampling highly skewed populations, such as those arising in many business surveys. Traditional Poisson πps sampling is a special case of PoMix sampling, but some PoMix designs are considerably more efficient than Poisson πps. When used with common estimators, some PoMix designs can lead to a considerably lower variance than Poisson πps. PoMix sampling gives a random sample size, regarded by some as a disadvantage. Therefore, we create in this article a family of fixed size PoMix designs, by using the central idea in order sampling: The population units are ordered by a ranking variable, and the sample consists of the n units with the smallest ranking variable values. This article reports results of a Monte Carlo simulation, where fixed size PoMix sampling is found to outperform other fixed size πps designs, and where (less surprisingly) regression and ratio estimators outperform the Horvitz-Thompson estimator. We show that the variance advantage of PoMix sampling is explained by a pronounced population skewness combined with a mildly heteroscedastic variance around the linear regression line.
Business surveys; permanent random numbers; skewed populations; fixed sample size.