Indirect sampling applied to skewed populations

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Pierre Lavallée and Sébastien Labelle-Blanchet¹

Abstract

Indirect Sampling is used when the sampling frame is not the same as the target population, but related to the latter. The estimation process for Indirect Sampling is carried out using the Generalised Weight Share Method (GWSM), which is an unbiased procedure (see Lavallée 2002, 2007). For business surveys, Indirect Sampling is applied as follows: the sampling frame is one of establishments, while the target population is one of enterprises. Enterprises are selected through their establishments. This allows stratifying according to the establishment characteristics, rather than those associated with enterprises. 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 GWSM results in unbiased estimates, but their variance can 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 describe the required adjustments to the GWSM. The estimates produced with these adjustments are compared to those from the original GWSM, via a small numerical example, and using real data originating from the Statistics Canada's Business Register.

Key Words

Generalised weight share method; Weighted links; Weak optimality.

Table of content

1 Introduction

2 Indirect sampling and the GWSM

3 The problem with skewed populations

4 Proposed methods

5 Simulations using real data

6 Conclusion

 

 

 

 

 

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¹  Pierre Lavallée, Business Survey Methods Division, Statistics Canada. E-mail: pierre.lavallee@statcan.gc.ca; Sébastien Labelle-Blanchet, Household Survey Methods Division, Statistics Canada. E-mail: sebastien.labelle-blanchet@statcan.gc.ca.