Variance Estimation from Complex Survey Designs: A Case Study of Household Income and Expenditure Survey Design 2002/03, Botswana

Abstract

In large-scale surveys, it is common to use a multistage sampling design, where the first-stage units are selected with varying probability without replacement and the second-stage units are selected according to the systematic sampling procedure. It is however well known that this sampling design makes it impossible to find unbiased estimate of the variance of the estimate of the population total. In this paper, a few methods of variance estimation in multistage sampling involving systematic sampling design have been proposed to overcome the problem discussed. The proposed variance estimators are compared with the few conventional methods, for example, Random group, Jackknife, as well as the method used by the Central Statistical Office (CSO) using the live data based on Household Income and Expenditure Survey (HIES) 2002/03, Botswana, collected by CSO. It is found that all the proposed methods and Jackknife method perform better than the method used by CSO.

Keywords:

• Complex survey design
• Inclusion probability proportional to size
• Jackknife method
• Random group method
• Variance estimation

Mathematics Subject Classification:

• 62 D05

Acknowledgment

The authors wish to thank the associate editor and the two anonymous referees for their valuable suggestions, specifically which lead to the inclusion of Table 3, which has led to a drastic improvement of the earlier version of this manuscript.