서베이앤헬스폴리시리서치센터

Kim, S. W., Heeringa, S. G., and Solenberger, P.W. (2005). “An empirical comparison of efficiency between optimization and non-optimization probability sampling of two units from a stratum,” in Proceedings of the Survey Research Methods Section, American Statistical Association, 3211-3219, Minneapolis, Minnesota: Joint Statistical Meetings.

Abstract

Survey samplers seek sampling designs providing a smaller variance as well as a more stable variance estimator for certain estimators of the population total. To achieve sample selections with these desirable properties, Kim, Heeringa, and Solenberger (2003, 2004) suggested several inclusion probability proportional to size sampling schemes. These optimization approaches use nonlinear programming (NLP) and are useful to select two units per stratum as is commonly done in the primary stage of a multi-stage design. Their NLP approaches highly depend on linear constraints that are based on the inclusion probabilities. In this paper, we first introduce the relationships between the linear constraints and the variances or variance estimators for existing sampling strategies such as probability proportional to size sampling with replacement and the methods of Brewer, Murthy, and Hanurav. Second, we examine the feasibility of NLP approaches related to those strategies for a set of natural populations. Finally, we compare the efficiency of the various estimators and variance estimators for those populations. We conclude that NLP approaches work well in comparison to the alternatives. 

Key words: Nonlinear Programming, Linear Constraints, Inclusion Probabilities, IPPS Sampling