Indirect Sampling Applied to Skewed Populations
Pierre Lavallée, Sébastien Labelle-Blanchet
Business Survey Methods Division, Statistics Canada, Ottawa, ON, Canada

Indirect Sampling is used when the sampling frame is not the same as the target population, but still related to the latter. The estimation process for Indirect Sampling is then performed using the Generalised Weight Share Method (GWSM), which produces unbiased estimates (see Lavallée, 2002, 2007). For economic surveys, Indirect Sampling is often applied in the context of a sampling frame of establishments, and a target population of enterprises. The selection of enterprises is made through the selection of a sample of some of their establishments. This allows, for instance, stratifying the selection process according to establishment characteristics, rather than enterprise ones. Because the variables of interest of establishments are generally highly skewed (a small portion of the establishments covers the major portion of the economy), the use of the GWSM still produces unbiased estimates, but the variance of these can happen to be large. The purpose of this paper is to suggest some adjustments to the weights to reduce the variance of the estimates in the context of skewed populations, while keeping the method unbiased. After a brief overview of Indirect Sampling and the GWSM, we will describe the proposed adjustments to be done to the GWSM. The estimates produced with these adjustments will then be compared to those from the original GWSM, both theoretically and empirically. The study uses real data from the Statistics Canada's Business Register.

Keywords: Generalised weight share method; Weighted links; Unbiased estimation; Weak optimality

Biography: Pierre Lavallée is working at Statistics Canada since 1985. He worked as a survey methodologist in social, business and farm surveys, as well as in the use of administrative data. He is presently Assistant-Director at the Business Survey Methods Division. He received his Ph.D. in 2001 from the Université Libre de Bruxelles (Belgium) for his thesis on Indirect Sampling.